Question

Find the vertex and write the quadratic function in vertex form (which our OpenStax textbook also calls the standard form).f(x)=x^2−12 x + 136 Give the vertex. Enter your answer as a point (a,b).Vertex: Preview Enter the coordinates of the vertex to write f(x) in vertex form:f(x)=(x− )2+

Answer 1

In an equation in the form:

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

The x-coordinate of the vertex is given by the next formula:

$x=-\frac{b}{2a}$

And the y coordinate of the vertex y the value of f in that x.

For the given function:

$f(x)=x^2-12x+136$

x-coordinate of the vertex:

$x=-\frac{(-12)}{2(1)}=\frac{12}{2}=6$

y-coordinate of the vertex:

$\begin{gathered} f(6)=(6)^2-12(6)+136 \\ f(6)=36-72+136 \\ f(6)=100 \end{gathered}$

Vertex: (6,100)

Vertex form of a quadratic function:

$\begin{gathered} f(x)=a(x-h)^2+k \\ \\ \text{Vertex: (h,k)} \end{gathered}$

For the given function the vertex form is:

$f(x)=(x-6)^2+100$

Graph with the vertex: