Question

which function has zeros at x = 10 and x = 2?
a) ( f(x) = x^2 - 12x + 20 )
b) ( f(x) = x^2 - 20x + 12 )
c) ( f(x) = 5x^2 + 40x + 60 )
d) ( f(x) = 5x^2 + 60x + 100 )

Explanation:

Step1: Use zero form of quadratic

If zeros are $x=10$ and $x=2$, the function is $f(x)=a(x-10)(x-2)$ where $a$ is a constant.

Step2: Expand the factored form

First multiply $(x-10)(x-2)$:
$$(x-10)(x-2)=x^2-2x-10x+20=x^2-12x+20$$

Step3: Match with given options

When $a=1$, the function matches the first option. Verify by substituting zeros:
For $x=10$: $f(10)=10^2-12(10)+20=100-120+20=0$
For $x=2$: $f(2)=2^2-12(2)+20=4-24+20=0$

Answer:

$f(x) = x^2 - 12x + 20$