Let f be a function defined by f(x)=5x²-4. Evaluate the following f (4)+f (-4)=

Given the function \( f(x) = 5x^2 - 4 \), we want to evaluate \( f(4) + f(-4) \).

1. **Evaluate \( f(4) \)**:
   \[
   f(4) = 5(4)^2 - 4
   \]
   \[
   = 5(16) - 4
   \]
   \[
   = 80 - 4 = 76
   \]

2. **Evaluate \( f(-4) \)**:
   \[
   f(-4) = 5(-4)^2 - 4
   \]
   \[
   = 5(16) - 4
   \]
   \[
   = 80 - 4 = 76
   \]

3. **Add the results**:
   \[
   f(4) + f(-4) = 76 + 76 = 152
   \]

So, \( f(4) + f(-4) = 152 \).

Would you like more details or have any questions? Here are some related questions you might find helpful:

1. What is the value of \( f(0) \)?
2. How would the function change if it was \( f(x) = 5x^2 + 4 \)?
3. What is the vertex of the parabola represented by \( f(x) = 5x^2 - 4 \)?
4. How do you find the roots of the equation \( f(x) = 0 \)?
5. What is the derivative of the function \( f(x) = 5x^2 - 4 \)?

**Tip**: For any quadratic function \( ax^2 + bx + c \), substituting \( x \) with a positive or negative value yields the same result for the \( x^2 \) term because squaring a number makes it positive.

Learn how to evaluate the quadratic function f(x) = 5x^2 - 4 at x = 4 and x = -4 with step-by-step calculations. Understand the process of function evaluation and its application in quadratic functions. Suitable for Grades 7-9 students studying quadratic equations.

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