Let's substitute \( x = -2 \) into the given function \( f(x) = 8x^2 - 9x + 3 \) and solve for \( f(-2) \).

\[
f(-2) = 8(-2)^2 - 9(-2) + 3
\]
First, calculate the powers and products:
\[
(-2)^2 = 4
\]
\[
8 \times 4 = 32
\]
\[
-9 \times (-2) = 18
\]

Now substitute these values back into the expression:
\[
f(-2) = 32 + 18 + 3 = 53
\]

Thus, \( f(-2) = 53 \).

Would you like more details or have any questions?

Here are five related questions to consider:
1. What is the vertex of the parabola represented by \( f(x) = 8x^2 - 9x + 3 \)?
2. How would you find the roots of \( f(x) = 8x^2 - 9x + 3 \)?
3. What is the axis of symmetry for the quadratic function \( f(x) \)?
4. How does the graph of \( f(x) = 8x^2 - 9x + 3 \) compare to \( f(x) = x^2 \)?
5. How would the function change if the coefficient of \( x^2 \) became negative?

**Tip:** To quickly find the output of a function, substitute the given value of \( x \) into the function and simplify step by step.

Learn how to evaluate the quadratic function f(x) = 8x^2 - 9x + 3 at x = -2 with a detailed step-by-step solution. This problem covers key algebraic concepts, such as substitution into quadratic functions, and is suitable for students in Grades 8-10.

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