Question

For what values of x is each function increasing? For what values of x is it decreasing? a. f(x) = x2 - 4x​

Answer 1

Answer:

to the right of x = 2 the function is increasing

{ x | x > 2}

Step-by-step explanation:

Recall that this is a quadratic function, and therefore responds to the shape of a parabola. In this case is also a parabola with branches opening up since the coefficient of the square term is positive. So, we just need to find where the vertex is located, and we know that to the left of the x-value of the vertex the function is decreasing, and to the right of it the function is increasing.

The formula for the x of the vertex of a parabola of the form:

$y=ax^2+bx+c$

is  $x_{vertex}=\frac{-b}{2\,a}$

which in our case gives:

$x_{vertex}=\frac{-b}{2\,a} =\frac{4}{2} =2$

Therefore, to the left of x = 2 the function decreases , and to the right of x = 2 the function is increasing.