Math Problem Statement

If h(x) = ax2 + 6 and h(-2) = -2, what is the value of a?

(A) -4

(B) -2

(C) 2

(D) 4

Solution

We are given the function h(x)=ax2+6h(x) = ax^2 + 6 and the value h(2)=2h(-2) = -2. To find the value of aa, we substitute x=2x = -2 into the equation and solve for aa.

Step-by-step:

  1. The given function is: h(x)=ax2+6h(x) = ax^2 + 6 Substituting x=2x = -2 into the function: h(2)=a(2)2+6h(-2) = a(-2)^2 + 6 h(2)=a(4)+6=4a+6h(-2) = a(4) + 6 = 4a + 6

  2. We know that h(2)=2h(-2) = -2, so: 4a+6=24a + 6 = -2

  3. Solving for aa: 4a=264a = -2 - 6 4a=84a = -8 a=84=2a = \frac{-8}{4} = -2

So, the value of aa is 2\boxed{-2}.

Answer: (B) -2

Would you like further details or clarifications?

Here are 5 related questions to explore:

  1. What is the value of h(3)h(3) if h(x)=2x2+6h(x) = -2x^2 + 6?
  2. How would the graph of h(x)=2x2+6h(x) = -2x^2 + 6 look compared to h(x)=x2h(x) = x^2?
  3. What would happen to the value of aa if the constant term changed from 6 to another number?
  4. How do you determine the vertex of a quadratic function like h(x)=ax2+ch(x) = ax^2 + c?
  5. How does changing aa in ax2ax^2 affect the shape of the parabola?

Tip: When solving quadratic equations, always carefully substitute given values for xx and h(x)h(x) before solving for unknowns like aa.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions

Formulas

h(x) = ax^2 + c
Substitution Method

Theorems

Basic Quadratic Function

Suitable Grade Level

Grades 8-10