Question

The graph of a quadratic function has x-intercepts of -7and -1 ,and passes through the point (-4,36). determine the equation of the quadratic function in the form f(x)=a(x-m)(x-n)

Answer 1

`f(x) = -4(x+7)(x+1)`

Explanation:

Quadratic equation:

A quadratic equation, with roots(x-intercepts) at
`x_1` and
`x_2`, and leading coefficient a, is given by:

`f(x) = a(x - x_1)(x - x_2)`

Has x-intercepts of -7 and -1

So
`x_1 = -7, x_2 = -1`. Thus

`f(x) = a(x - (-7))(x - (-1)) = a(x+7)(x+1)`

Passes through the point (-4,36).

This means that when
`x = -4, y = 36`, and we use this to find the leading coefficient.

`36 = a(-4+7)(-4+1)`

`a(3)(-3) = 36`

`-9a = 36`

`a = -(36)/(9)`

`a = -4`

So

`f(x) = -4(x+7)(x+1)`