Question

If `f(x)=4x^2-24x+36`, how do you find the value f(x)=4?

Answer 1

You know that your function looks like this

`f(x) = 4x^2 - 24x + 36`

If `f(x) = 4`, then you can say that

`f(x) = 4x^2 - 24x + 36 = 4`

Get this equation in quadratic form by adding `-4` to both sides of the equation

`4x^2 - 24x + 36 - 4= color(red)(cancel(color(black)(4))) - color(red)(cancel(color(black)(4)))`

`4x^2 - 24x + 32 = 0`

This is equivalent ot

`4(x^2 - 6x + 8) = 0`

You can use the quadratic formula to get the two solutions for this equation

`x_(1,2) = (-(-6) +- sqrt((-6)^2 - 4 * 1 * 8))/2`

`x_(1,2) = (6 +- sqrt(36 - 32))/2`

`x_(1,2) = (6 +- 2)/2 = {(x_1 = 4), (x_2 = 2) :}`

This means that you have two values of `x` for which `f(x)` is equal to `4`.

`f(2) = 4` and `f(4) = 4`