Question

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!

Answer 1

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.

Question 1

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.

Question 2

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).