교과서 질문
Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. (x+1)(x+2)(x+3)≥0
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Ch. 3 - Polynomial and Rational Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
4장, 문제 29
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)=x2+3x−10
검증된 단계별 안내1
Identify the quadratic function given: \(f(x) = x^2 + 3x - 10\).
Find the vertex of the parabola using the formula for the x-coordinate of the vertex: \(x = -\frac{b}{2a}\), where \(a = 1\) and \(b = 3\).
Calculate the y-coordinate of the vertex by substituting the x-value found into the function: \(f\left(-\frac{b}{2a}\right)\).
Find the x-intercepts by solving the quadratic equation \(x^2 + 3x - 10 = 0\) using factoring or the quadratic formula.
Determine the y-intercept by evaluating \(f(0)\), then write the equation of the axis of symmetry as \(x = -\frac{b}{2a}\), and use the vertex and intercepts to describe the domain and range of the function.
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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
2m주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Vertex of a Quadratic Function
The vertex is the highest or lowest point on the parabola, representing its maximum or minimum value. It can be found using the formula x = -b/(2a) for a quadratic function f(x) = ax² + bx + c. The vertex helps in sketching the graph and determining the axis of symmetry.
추천 영상:
08:07
Vertex Form
Intercepts of a Quadratic Function
Intercepts are points where the graph crosses the axes. The y-intercept is found by evaluating f(0), and the x-intercepts (roots) are found by solving f(x) = 0. These points provide key reference locations for sketching the parabola accurately.
추천 영상:
06:36Solving Quadratic Equations Using The Quadratic Formula
Domain and Range of a Quadratic Function
The domain of any quadratic function is all real numbers since x can take any value. The range depends on the vertex: if the parabola opens upward, the range is all values greater than or equal to the vertex's y-coordinate; if downward, all values less than or equal to it. This helps describe the function's output values.
추천 영상:
4:22Domain & Range of Transformed Functions
관련 실천
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In Exercises 27–29, divide using long division.
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교과서 질문
Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. (x−1)(x−2)(x−3)≥0
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교과서 질문
Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. n=4; i and 3i are zeros; f(-1) = 20
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교과서 질문
Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. f(x)=(x2−9)/(x−3)
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교과서 질문
Divide using synthetic division. (x4−256)/(x−4)
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