Identify the zeros of the functions. 1. y = 5(x - 3)(x + 5) 2. y = (x - 7)^2 Help with these problems above would be greatly appreciated, thanks!

Question

asked Nov 10, 2023 185k views

1 Answer

Seong · Answer 1 · 2023-11-16T20:33:21+0000

Answer:

1. 3 and -5

2. 7

Explanation:

The zeros of functions are the x-values when y = 0, i.e the point(s) at which the line crosses the x-axis.

To find the zeros of the given functions, set the function to zero and solve for x.

Given function:

y=5(x-3)(x+5)

Set the function to zero:

$\implies 5(x-3)(x+5)=0$

$\implies (5(x-3)(x+5))/(5)=(0)/(5)\\$

$\implies (x-3)(x+5)=0$

Using the Zero Product Property, set each factor equal to zero and solve for x:

$\implies (x-3)=0 \implies x=3$

$\implies (x+5)=0 \implies x=-5$

Therefore, the zeros of the function are 3 and -5.

Given function:

y=(x-7)^2

Set the function to zero and solve for x

$\implies (x-7)^2=0$

$\implies √((x-7)^2)=√(0)$

$\implies x-7=0$

$\implies x=7$

Therefore, the zero of the function is 7 (with multiplicity 2).