Let's solve the function \( y = 3x^4 - 2x^2 + 8 \) step by step for a specific value of \( x \).
### Step-by-Step Solution:
1. Identify the function:
\( y = 3x^4 - 2x^2 + 8 \)
2. Choose a value for \( x \):
Let's take \( x = 2 \) as our example value.
3. Substitute \( x = 2 \) into the function:
[tex]\[
y = 3(2)^4 - 2(2)^2 + 8
\][/tex]
4. Compute \( 2^4 \):
[tex]\[
2^4 = 16
\][/tex]
5. Plug this back into the equation:
[tex]\[
y = 3 \cdot 16 - 2(2^2) + 8
\][/tex]
6. Compute \( 3 \cdot 16 \):
[tex]\[
3 \cdot 16 = 48
\][/tex]
7. Compute \( 2^2 \):
[tex]\[
2^2 = 4
\][/tex]
8. Compute \( 2 \cdot 4 \):
[tex]\[
2 \cdot 4 = 8
\][/tex]
9. Substitute these values back into the function:
[tex]\[
y = 48 - 8 + 8
\][/tex]
10. Simplify the expression:
[tex]\[
y = 48 - 8 + 8 = 48
\][/tex]
So, for \( x = 2 \), the value of the function \( y = 3x^4 - 2x^2 + 8 \) is \( y = 48 \).
Therefore, the result is
[tex]\[
y = 48
\][/tex]
