Question

The equation of a parabola is given.

y=16x2+2x+11

What are the coordinates of the vertex of the parabola?

Enter your answer in the boxes.

( , )

Answer 1

The answer is (0,11). Find x and Find y by using 0 for one variable when solving for another and you have your answer.

Answer 2

`(-6,5)`

Explanation:

We have been given an equation of a parabola
`y=(1)/(6)x^2+2x+11`. We are asked to find the coordinates of the vertex of our given parabola.

We will use
`(-b)/(2a)` formula to find the x-coordinate of parabola.

Upon substituting our given values in above formula we will get,

`(-2)/(2* (1)/(6))`

`(-1)/((1)/(6))`

`(-1* 6)/(1* 1)=-6`

Now, we will substitute
`x=-6` in our given equation to find the y-coordinate of the vertex.

`y=(1)/(6)(-6)^2+2(-6)+11`

`y=(1)/(6)*36-12+11`

`y=1*6-12+11`

`y=6-12+11`

`y=5`

Therefore, the coordinates of the vertex of our given parabola are
`(-6,5)`.