Question

write a quadratic function with zeros -9 and -3.
write your answer using the variable x and in standard form with a leading coefficient of 1.

f(x) =
2 3 4

Explanation:

Step1: Use zero factor form

If $r_1$ and $r_2$ are zeros of a quadratic function, the function can be written as $f(x)=(x-r_1)(x-r_2)$. Here, $r_1=-9$ and $r_2=-3$, so substitute these values:
$f(x)=(x-(-9))(x-(-3))=(x+9)(x+3)$

Step2: Expand the binomials

Use the FOIL method to multiply $(x+9)(x+3)$:
$f(x)=x\cdot x + x\cdot3 + 9\cdot x + 9\cdot3$

Step3: Simplify the expression

Combine like terms and compute products:
$f(x)=x^2 + 3x + 9x + 27 = x^2 + 12x + 27$

Answer:

$f(x)=x^2 + 12x + 27$