Find a formula for a quadratic function whose graph has x-intercepts at (1, 0) and (5, 0), and y-intercept at (0, 7).

Guest Feb 8, 2021

#1**0 **

The x-intercepts are at (1, 0) and (5, 0). This means the roots of the quadratic function are 1 and 5.

We can be sure that the quadratic function is of the form \(f(x) = C (x - 1)(x - 5)\) where C is a constant.

We can substitute the point (x, f(x)) = (0, 7) into the equation to find C.

7 = C (-1)(-5)

C = 7/5.

Therefore \(f(x) = \dfrac 75 (x - 1)(x - 5)\)

MaxWong Feb 8, 2021