Question

Which equation, when graphed, has x-intercepts at (2.0) and (40) and a y-intercept of (0, -16)?

f(x) = -(x - 2)(x-4)
f(x) = -(x + 2)(x + 4)
f(x) = -2(x - 2)(x - 4)
f(x) = -2(x + 2)(x + 4)
N
Mark this and return
Save and Exit
Im Next
>
Submit

Answer 1

`f(x)=-2(x-2)(x-4)`

Explanation:

If the equation, when graphed, has x-intercepts at (2,0) and (4,0), then it is of the form

`f(x)=a(x-2)(x-4)`

Open the brackets:

`f(x)=a(x^2-2x-4x+8)\\ \\f(x)=a(x^2-6x+8)\\ \\f(x)=ax^2-6ax+8a`

This equation has y-intercept at (0,-16), then whan x = 0, f(x) =-16:

`-16=a\cdot 0^2-6a\cdot 0+8a\\ \\8a=-16\\ \\a=-2`

Therefore,

`f(x)=-2(x-2)(x-4)`