Question

Determine the quadratic function, f(x), with x intercepts at x=7 and x=-2 and y intercept at y=5.

I have been struggling with this question for days. I have phoned my teacher and gotten her help, but I still can't figure it out. If someone could please help me with this, that would be great. Thanks

Answer 1

For days ????

since the x-intercepts of a function are the same as the roots of the corresponding equation
x=7 ----> a factor of (x-7)
x=-2 ---> a factor of (x+2)

so f(x) = a(x-7)(x+2)
we are told that (0,5) lies on it, so
5 = a(-7)(2)
a = -5/14

f(x) = (-5/14)(x-7)(x+2)
or
f(x) = (-5/14)x^2 - (25/14)x + 5

check:
https://www.wolframalpha.com/input/?i=solve+(-5%2F14)x%5E2+-+(25%2F14)x+%2B+5%3D0