Quadratic Functions: 동영상 및 연습문제

Which of the following graphs of a quadratic function satisfies the condition given below?

a < 0; b² - 4ac = 0

Which of the following graphs of a quadratic function satisfies the condition given below?

a < 0; b² - 4ac < 0

Which of the following graphs of a quadratic function satisfies the condition given below?

a > 0; b² - 4ac > 0

Determine a quadratic function f(x) for the graph given below.

Determine a quadratic function f(x) for the graph given below.

For the following quadratic function, determine the value of c so that it has only one x-intercept.

y = x² - 16x + c

For the following quadratic function, determine the values of a so that it has no x-intercepts.

y = ax² - 18x + 13

Find a quadratic function that satisfies the following conditions.

x-intercepts: (4, 0) and (7, 0)

y-intercept: (0, 14)

Find the other zero of the quadratic equation if one of the zeros is 4 given that the vertex of the function is (8, 4).

Find the coordinates of the closest point on the line y = 3x to the point (2, 14). Use the distance formula.

A ball is thrown upward from the roof of a building with an initial velocity of 16 ft/sec. The height of the building is 50 ft. The equation for the height of the ball after t seconds is given as s(t) = -16t² + 16t + 50. Determine the time when the ball will achieve a maximum height. Also, find the maximum height.

Choose the correct option to fill in the blanks. In the quadratic equation y=a(x - h)² + k, if a > 0, the graph opens _____.

Choose the correct option to fill in the blanks. The y-coordinate of the vertex of the graph of y = x² -24x +149 is ____. 

Graph the quadratic function and find out the vertex, axis, domain, and range of the quadratic function.

h(x) = (x - 11)² -2

Graph the quadratic function and find out the vertex, axis, domain, and range of the quadratic function. 

h(x) = -(1/3)(x +3)² -12

Graph the quadratic function and find out the vertex, axis, domain, and range of the quadratic function.

h(x) = -6(x -7)² +1

Graph the quadratic function and find out the vertex, axis, domain, and range of the quadratic function.

h(x) = x² + 12x + 11

Graph the quadratic function and find out the vertex, axis, domain, and range of the quadratic function.

h(x) = -9x² + 54x -76

Find out the domain and range for the graph of the given quadratic function.

Find out the domain and range for the graph of the given quadratic function.

Find the graph of the quadratic function.

ƒ(x) = (x - 7)² - 9

Find the graph of the quadratic function.

ƒ(x) = (x +7)² - 9

Consider the quadratic function f(x) = -2x² + 16x - 14 and graph it. With the aid of the graph, identify the largest open intervals within its domain at which it is increasing and decreasing. Also, determine its x and y-intercepts, axis of symmetry, vertex, domain, and range.

In a certain university, the number of students who participated in the yearly fundraising activity from 2011 to 2018 can be modeled by A(x) = 3x² - 52x + 255, where x = 1 represents the year 2011. From 2018 to 2022, the number of students is represented by A(x) = 42x - 305. Calculate the number of students who participated in the activity in 2011.

In a certain university, the number of students who participated in the yearly fundraising activity from 2011 to 2018 can be modeled by A(x) = 3x² - 52x + 255, where x = 1 represents the year 2011. From 2018 to 2022, the number of students is represented by A(x) = 42x - 305. Calculate the number of students who participated in the activity in 2015.

In a certain university, the number of students who participated in the yearly fundraising activity from 2011 to 2018 can be modeled by A(x) = 3x² - 52x + 255, where x = 1 represents the year 2011. From 2018 to 2022, the number of students is represented by A(x) = 42x - 305. Calculate the number of students who participated in the activity in 2018.

In a certain university, the number of students who participated in the yearly fundraising activity from 2011 to 2018 can be modeled by A(x) = 3x² - 52x + 255, where x = 1 represents the year 2011. From 2018 to 2022, the number of students is represented by A(x) = 42x - 305. Calculate the number of students who participated in the activity in 2020.

In a certain university, the number of students who participated in the yearly fundraising activity from 2011 to 2018 can be modeled by A(x) = 3x² - 52x + 255, where x = 1 represents the year 2011. From 2018 to 2022, the number of students is represented by A(x) = 42x - 305. Graph y = A(x) for the years 2011 to 2022 and determine the year in which the number of students who participated is the least.

Sketch the graph of the parabola defined by f(x) = (x + 1)² - 4 by using its vertex and intercepts. Identify the domain and range based from the drawn graph, and identify the equation for the axis of symmetry.

Sketch the graph of the parabola defined by f(x) = -x² - 8x - 12 by using its vertex and intercepts. Identify the domain and range based from the drawn graph, and identify the equation for the axis of symmetry.