Question

for quadratic function f, the solutions to the equation f(x) = 0 are x = 8 and x = -4. Which function could represent f?
a f(x) = x^2 + 4x - 32
b f(x) = x^2 + 12x + 32
c f(x) = x^2 - 4x - 32
d f(x) = x^2 - 12x + 32

Answer 1

To find the quadratic function \( f(x) \) that has solutions \( x = 8 \) and \( x = -4 \), we can use the fact that a quadratic function can be expressed in factored form based on its roots.

The roots can be used to write \( f(x) \) as:

\[
f(x) = a(x - 8)(x + 4)
\]

For convenience, we can choose \( a = 1 \):

\[
f(x) = (x - 8)(x + 4)
\]

Now we can expand this:

\[
f(x) = x^2 + 4x - 8x - 32
\]
\[
f(x) = x^2 - 4x - 32
\]

Now, let's compare this with the given options:

a) \( f(x) = x^2 + 4x - 32 \)
b) \( f(x) = x^2 + 12x + 32 \)
c) \( f(x) = x^2 - 4x - 32 \)
d) \( f(x) = x^2 - 12x + 32 \)

The correct function that represents \( f \) is:

**c) \( f(x) = x^2 - 4x - 32 \)**.