`h(x)=cx^(2)+18`
For the function h defined above, c is constant and h(2)=10. what is the value of h(-2)?

Options

A. `-10`
B. `-2`
C. `10`
D. `18`

Answer

To solve the problem step by step, we will follow the process outlined in the video transcript.

### Step 1: Understand the function and the given condition
The function is defined as:
\[ h(x) = cx^2 + 18 \]
We are given that \( h(2) = 10 \).

### Step 2: Substitute \( x = 2 \) into the function
Using the given condition, we substitute \( x = 2 \) into the function:
\[ h(2) = c(2^2) + 18 \]
This simplifies to:
\[ h(2) = c(4) + 18 \]

### Step 3: Set up the equation using the given value of \( h(2) \)
Since we know that \( h(2) = 10 \), we can set up the equation:
\[ 4c + 18 = 10 \]

### Step 4: Solve for \( c \)
Now, we will isolate \( c \):
1. Subtract 18 from both sides:
\[ 4c = 10 - 18 \]
\[ 4c = -8 \]
2. Divide both sides by 4:
\[ c = \frac{-8}{4} \]
\[ c = -2 \]

### Step 5: Rewrite the function with the value of \( c \)
Now that we have found \( c \), we can rewrite the function:
\[ h(x) = -2x^2 + 18 \]

### Step 6: Calculate \( h(-2) \)
Next, we need to find \( h(-2) \):
\[ h(-2) = -2(-2)^2 + 18 \]
This simplifies to:
\[ h(-2) = -2(4) + 18 \]
\[ h(-2) = -8 + 18 \]
\[ h(-2) = 10 \]

### Final Answer
Thus, the value of \( h(-2) \) is:
\[ \boxed{10} \]

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