Answer:
The x-intercepts of the quadratic function are 8 and -4.
Step-by-step explanation:
The given function is
[tex]f(x)=x^2-4x-32[/tex]
Equate the function f(x) equal to 0, to find the x-intercepts of the quadratic function.
[tex]f(x)=0[/tex]
[tex]x^2-4x-32=0[/tex]
The middle term can be written as -8x+4x.
[tex]x^2-8x+4x-32=0[/tex]
[tex]x(x-8)+4(x-8)=0[/tex]
Take out the common factors.
[tex](x-8)(x+4)=0[/tex]
Using zero product property,
[tex]x-8=0\Rightarrow x=8[/tex]
[tex]x+4=0\Rightarrow x=-4[/tex]
Therefore the x-intercepts of the quadratic function are 8 and -4.
