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

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Answer 1 · 2015-07-27T12:20:52

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 $f(4) = 4$

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