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

(A) -4

(B) -2

(C) 2

(D) 4

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

### Step-by-step:

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

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

3. Solving for \( a \):
   \[
   4a = -2 - 6
   \]
   \[
   4a = -8
   \]
   \[
   a = \frac{-8}{4} = -2
   \]

So, the value of \( a \) is \( \boxed{-2} \).

### Answer: (B) -2

Would you like further details or clarifications?

Here are 5 related questions to explore:
1. What is the value of \( h(3) \) if \( h(x) = -2x^2 + 6 \)?
2. How would the graph of \( h(x) = -2x^2 + 6 \) look compared to \( h(x) = x^2 \)?
3. What would happen to the value of \( a \) if the constant term changed from 6 to another number?
4. How do you determine the vertex of a quadratic function like \( h(x) = ax^2 + c \)?
5. How does changing \( a \) in \( ax^2 \) affect the shape of the parabola?

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

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

(A) -4

(B) -2

(C) 2

(D) 4

Learn how to solve for 'a' in the quadratic function h(x) = ax^2 + 6 given h(-2) = -2. This problem demonstrates substitution in quadratic functions and is suitable for students in Grades 8-10.

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