Multiple ChoiceIdentify the ordered pair of the vertex of the parabola. State whether it is a minimum or maximum.391Has a video solution.
Multiple ChoiceGraph the given quadratic function. Identify the vertex, axis of symmetry, intercepts, domain, range, and intervals for which the function is increasing or decreasing. f(x)=−(x−5)2+1f\left(x\right)=-\left(x-5\right)^2+1f(x)=−(x−5)2+1231Has a video solution.
Multiple ChoiceGraph the given quadratic function. Identify the vertex, axis of symmetry, intercepts, domain, range, and intervals for which the function is increasing or decreasing. f(x)=3x2+12xf\left(x\right)=3x^2+12xf(x)=3x2+12x54Has a video solution.
Textbook QuestionIn Exercises 1–4, the graph of a quadratic function is given. Write the function's equation, selecting from the following options. 116Has a video solution.
Textbook QuestionIn Exercises 1–4, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation for the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x) = - (x + 1)^2 + 447Has a video solution.
Textbook QuestionIn Exercises 1–4, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation for the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x) = (x + 4)^2 - 2110Has a video solution.
Textbook QuestionIn Exercises 1–4, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation for the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x) = -x^2 +2x + 3101Has a video solution.
Textbook QuestionGraph each quadratic function. Give the vertex, axis, x-intercepts, y-intercept, domain, range, and largest open intervals of the domain over which each function is increasing or decreasing. ƒ(x)=-3x^2-12x-144Has a video solution.
Textbook QuestionIn Exercises 1–4, the graph of a quadratic function is given. Write the function's equation, selecting from the following options. 43Has a video solution.
Textbook QuestionFill in the blank(s) to correctly complete each sentence. The highest point on the graph of a parabola that opens down is the ____ of the parabola.40Has a video solution.
Textbook QuestionFill in the blank(s) to correctly complete each sentence. The vertex of the graph of ƒ(x) = x^2 + 2x + 4 has x-coordinate ____ .36Has a video solution.
Textbook QuestionIn Exercises 5–8, the graph of a quadratic function is given. Write the function's equation, selecting from the following options. 27Has a video solution.
Textbook QuestionIn Exercises 5–6, use the function's equation, and not its graph, to find (a) the minimum or maximum value and where it occurs. (b) the function's domain and its range. f(x) = -x^2 + 14x - 10680Has a video solution.
Textbook QuestionIn Exercises 5–8, the graph of a quadratic function is given. Write the function's equation, selecting from the following options. 70Has a video solution.
Textbook QuestionSolve each problem. During the course of ayear, the number of volunteers available to run a food bank each month is modeled by V(x), where V(x)=2x^2-32x+150 between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, V(x) is mod-eled by V(x)=31x-226. Find the number of volunteers in each of the following months. Sketch a graph of y=V(x) for January through December. In what month are the fewest volunteers available?23Has a video solution.
Textbook QuestionSolve each problem. During the course of ayear, the number of volunteers available to run a food bank each month is modeled by V(x), where V(x)=2x^2-32x+150 between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, V(x) is mod-eled by V(x)=31x-226. Find the number of volunteers in each of the following months. January28Has a video solution.
Textbook QuestionSolve each problem. During the course of ayear, the number of volunteers available to run a food bank each month is modeled by V(x), where V(x)=2x^2-32x+150 between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, V(x) is mod-eled by V(x)=31x-226. Find the number of volunteers in each of the following months. October25Has a video solution.
Textbook QuestionSolve each problem. During the course of ayear, the number of volunteers available to run a food bank each month is modeled by V(x), where V(x)=2x^2-32x+150 between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, V(x) is mod-eled by V(x)=31x-226. Find the number of volunteers in each of the following months. December32Has a video solution.
Textbook QuestionSolve each problem. During the course of ayear, the number of volunteers available to run a food bank each month is modeled by V(x), where V(x)=2x^2-32x+150 between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, V(x) is mod-eled by V(x)=31x-226. Find the number of volunteers in each of the following months. August27Has a video solution.
Textbook QuestionSolve each problem. During the course of ayear, the number of volunteers available to run a food bank each month is modeled by V(x), where V(x)=2x^2-32x+150 between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, V(x) is mod-eled by V(x)=31x-226. Find the number of volunteers in each of the following months. May24Has a video solution.
Textbook QuestionIn Exercises 9–16, find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=2(x−3)^2+161Has a video solution.
Textbook QuestionAmong all pairs of numbers whose difference is 14, find a pair whose product is as small as possible. What is the minimum product?2741Has a video solution.
Textbook QuestionIn Exercises 9–16, find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=−2(x+1)^2+5106Has a video solution.
Textbook QuestionConsider the graph of each quadratic function.(a) Give the domain and range. 60Has a video solution.
Textbook QuestionConsider the graph of each quadratic function.(a) Give the domain and range. 43Has a video solution.
Textbook QuestionIn Exercises 9–16, find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=2x^2−8x+364Has a video solution.
Textbook QuestionIn Exercises 9–16, find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=−x^2−2x+8106Has a video solution.
Textbook QuestionMatch each function with its graph without actually entering it into a calculator. Then, after completing the exercises, check the answers with a calculator. Use the standard viewing window. ƒ(x) = (x - 4)^2 - 374Has a video solution.
Textbook QuestionMatch each function with its graph without actually entering it into a calculator. Then, after completing the exercises, check the answers with a calculator. Use the standard viewing window. ƒ(x) = (x + 4)^2 - 330Has a video solution.
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=(x−4)^2−142Has a video solution.
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=(x−1)^2+227Has a video solution.
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. y−1=(x−3)^225Has a video solution.
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=2(x+2)^2−134Has a video solution.
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=4−(x−1)^288Has a video solution.
Textbook QuestionGraph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. See Examples 1–4. ƒ(x) = (x - 5)^2 - 450Has a video solution.
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=x^2−2x−3135Has a video solution.
Textbook QuestionGraph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. See Examples 1–4. ƒ(x) = -1/2 (x + 1)^2 - 329Has a video solution.
Textbook QuestionGraph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. See Examples 1–4. ƒ(x) = -3 (x - 2)^2 +136Has a video solution.
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=x^2+3x−10300Has a video solution.
Textbook QuestionGraph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. See Examples 1–4. ƒ(x) = x^2 + 6x + 538Has a video solution.
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=2x−x^2+392Has a video solution.
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=x^2+6x+386Has a video solution.
Textbook QuestionGraph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. See Examples 1–4. ƒ(x) = -3x^2 + 24x - 4694Has a video solution.
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=2x^2+4x−385Has a video solution.
Textbook QuestionIn Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=2x−x^2−268Has a video solution.
Textbook QuestionIn Exercises 39–44, an equation of a quadratic function is given. a) Determine, without graphing, whether the function has a minimum value or a maximum value. b) Find the minimum or maximum value and determine where it occurs. c) Identify the function's domain and its range. f(x)=3x^2−12x−160Has a video solution.
Textbook QuestionIn Exercises 39–44, an equation of a quadratic function is given. a) Determine, without graphing, whether the function has a minimum value or a maximum value. b) Find the minimum or maximum value and determine where it occurs. c) Identify the function's domain and its range. f(x)=−4x^2+8x−3160Has a video solution.
Textbook QuestionIn Exercises 39–44, an equation of a quadratic function is given. a) Determine, without graphing, whether the function has a minimum value or a maximum value. b) Find the minimum or maximum value and determine where it occurs. c) Identify the function's domain and its range. f(x)=5x^2−5x76Has a video solution.
Textbook QuestionIn Exercises 45–48, give the domain and the range of each quadratic function whose graph is described. The vertex is and the parabola opens up.51Has a video solution.
Textbook QuestionSeveral graphs of the quadratic function ƒ(x) = ax^2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) a < 0; b^2 - 4ac = 029Has a video solution.
Textbook QuestionIn Exercises 45–48, give the domain and the range of each quadratic function whose graph is described. Maximum = -6 at x = 1048Has a video solution.
Textbook QuestionSeveral graphs of the quadratic function ƒ(x) = ax^2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) a < 0; ^b2 - 4ac < 0108Has a video solution.
Textbook QuestionIn Exercises 49–52, write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 2x^2 but with the given point as the vertex. (5, 3)71Has a video solution.
Textbook QuestionSeveral graphs of the quadratic function ƒ(x) = ax^2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) A > 0; b^2 - 4ac > 0115Has a video solution.
Textbook QuestionIn Exercises 49–52, write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 2x^2 but with the given point as the vertex. (−10, −5)48Has a video solution.
Textbook QuestionConnecting Graphs with Equations Find a quadratic function f having the graph shown. (Hint: See the Note following Example 3.) 46Has a video solution.
Textbook QuestionIn Exercises 53–56, write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 3x^2 or g(x) = -3x^2, but with the given maximum or minimum. Maximum = 4 at x = -282Has a video solution.
Textbook QuestionConnecting Graphs with Equations Find a quadratic function f having the graph shown. (Hint: See the Note following Example 3.) 80Has a video solution.
Textbook QuestionIn Exercises 53–56, write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 3x^2 or g(x) = -3x^2, but with the given maximum or minimum. Minimum = 0 at x = 1151Has a video solution.
Textbook QuestionAmong all pairs of numbers whose sum is 16, find a pair whose product is as large as possible. What is the maximum product?203Has a video solution.
Textbook QuestionAmong all pairs of numbers whose difference is 24, find a pair whose product is as small as possible. What is the minimum product?56Has a video solution.
Textbook QuestionHeight of an Object If an object is projected upward from an initial height of 100 ft with an initial velocity of 64 ft per sec, then its height in feet after t seconds is given by s(t) = -16t^2 + 64t + 100. Find the number of seconds it will take the object to reach its maximum height. What is this maximum height?55Has a video solution.
Textbook QuestionFind a value of c so that y = x^2 - 10x + c has exactly one x-intercept.69Has a video solution.
Textbook QuestionFor what values of a does y = ax^2 - 8x + 4 have no x-intercepts?24Has a video solution.
Textbook QuestionDefine the quadratic function ƒ having x-intercepts (2, 0) and (5, 0) and y-intercept (0, 5).116Has a video solution.
Textbook QuestionDefine the quadratic function ƒ having x-intercepts (1, 0) and (-2, 0) and y-intercept (0, 4).69Has a video solution.
Textbook QuestionThe distance between the two points P(x₁, y₁) and R(x₂, y₂) is d(P, R) = √(x₁ - x₂)^2 + (y₁ -y₂)^2. Distance formula. Find the closest point on the line y = 2x to the point (1, 7). (Hint: Every point on y = 2x has the form (x, 2x), and the closest point has the minimum distance.)46Has a video solution.
Textbook QuestionA quadratic equation ƒ(x) = 0 has a solution x = 2. Its graph has vertex (5, 3). What is the other solution of the equation?29Has a video solution.
Textbook QuestionIn Exercises 97–98, write the equation of each parabola in vertex form. Vertex: (-3,-4) The graph passes through the point (1,4).70Has a video solution.
Textbook QuestionIn Exercises 97–98, write the equation of each parabola in vertex form. Vertex: (-3,-1) The graph passes through the point (-2,-3).164Has a video solution.
