Question

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

Explanation:

Step1: Use zero-product property

If $x=1$ and $x=-9$ are zeros, then the function can be written as $f(x)=(x-1)(x+9)$

Step2: Expand the binomials

Multiply using FOIL method:

$$\begin{align*} f(x)&=x\cdot x + x\cdot9 -1\cdot x -1\cdot9\\ &=x^2 +9x -x -9 \end{align*}$$

Step3: Combine like terms

Simplify the linear terms:
$f(x)=x^2 +8x -9$

Answer:

$f(x)=x^2 +8x -9$