Math Problem Statement

A quadratic function has vertex at (-2, 4) and passes through the point (-1, 1). What are the values of a, h, and k in the vertex form f(x) = a(x - h)^2 + k? Also, a quadratic function has x-intercepts at (-3, 0) and (5, 0) with a range of [-3, ∞). What is the vertex of this quadratic function?

Solution

Let's go through each question in detail.

Question 8

A quadratic function has a vertex at (−2,4)(-2, 4) and passes through the point (−1,1)(-1, 1). The vertex form of a quadratic function is: f(x)=a(x−h)2+kf(x) = a(x - h)^2 + k where (h,k)(h, k) is the vertex of the function.

  1. Since the vertex is (−2,4)(-2, 4), we have:

    • h=−2h = -2
    • k=4k = 4

  2. Now, we need to find aa. We substitute

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Vertex Form of a Quadratic Equation
Intercepts
Range of a Function

Formulas

Vertex form of a quadratic function: f(x) = a(x - h)^2 + k

Theorems

Vertex and Intercept Properties of Quadratic Functions

Suitable Grade Level

Grades 9-11

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