Question

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

Answer 1

Answer:

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

Step-by-step 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,

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