Question

Write each function in vertex form, and identify its vertex.f(x)=2x^2+36x+157.

Answer 1

`f(x)=2(x+9)^2-5`

Step-by-step explanation:

The vertex form of a quadratic equation is given as:

`y=a(x-h)^2+k`

Given the equation

`f\mleft(x\mright)=2x^2+36x+157`

First, we rewrite it as follows:

`f\mleft(x\mright)-157=2x^2+36x`

Next, we factorize the right-hand side.

`f(x)-157=2(x^2_{}+18x)`

We complete the expression in the bracket at the right-hand side.

`f(x)-157+2(81)=2(x^2+18x+81)`

This then gives us:

`\begin{gathered} f(x)-157+162=2(x+9)^2 \\ f(x)+5=2(x+9)^2 \\ f(x)=2(x+9)^2-5 \end{gathered}`

The vertex form is:

`f(x)=2(x+9)^2-5`