Question

What are the x-intercepts of the quadratic function?

f(x)=x^2+2x−24



Enter your answers in the boxes.

____________ and ___________

Answer 1

x²+2x-24
x²+6x-4x-24
x(x+6) -4(x+6)
(x-4)(x+6)
zeros= x=4 and x=-6

Answer 2

x= -6 and x= 4

Explanation:

WE need to find x intercepts for the given quadratic function

`f(x)=x^2+2x-24`

To find x intercept we set f(x)=0 and solve for x

`0=x^2+2x-24`

To solve for x we need to factor x^2 +2x-24

We need to find out two factors whose product is -24 and sum is 2

6 times -4= -24 and 6-4= 2

Break the middle term 2x using factors 6x-4x

`0=x^2+6x-4x-24`

`0=(x^2+6x)+(-4x-24)`

`0=x(x+6)-4(x+6)`

0=(x+6)(x-4)

now we set each factor =0 and solve for x

x+6 =0 , so x=-6

x-4=0 so x= 4

x= -6 and x= 4