Question

What is the vertex of the quadratic function f(x) = (x - 6) (2x + 2)?

Answer 1

Answer:

the coordinates of the vertex are: (2.5, -24.5)

Step-by-step explanation:

Recall that when we have a quadratic in its standard form:

$f(x)=ax^2+bx+c$

the position of the x-coordinate for the vertex can be obtained via:

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

Then in order to find the vertex, first we write the expression in standard form:

$f(x)=(x-6)(2x+2)\\f(x)=2x^2+2x-12x-12\\f(x)=2x^2-10x-12$

Now that we have the values for the parameters "$a$" and "b" we find the x of the vertex:

$x_{vertex}=\frac{-b}{2a}=\frac{10}{2*2}=\frac{5}{2}$

Now we use this x-value in the function to find the correspondent y-value of the vertex:

$f(x)=2x^2-10x-12\\f(\frac{5}{2} )=2\,(\frac{5}{2} )^2-10(\frac{5}{2} )-12\\f(\frac{5}{2} )=-24.5$

Then, the coordinates of the vertex are: (2.5, -24.5)