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

Answer:

$(-6,5)$

Step-by-step explanation:

We have been given an equation of a parabola $y=\frac{1}{6}x^2+2x+11$. We are asked to find the coordinates of the vertex of our given parabola.

We will use $\frac{-b}{2a}$ formula to find the x-coordinate of parabola.

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

$\frac{-2}{2\times \frac{1}{6}}$

$\frac{-1}{\frac{1}{6}}$

$\frac{-1\times 6}{1\times 1}=-6$

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

$y=\frac{1}{6}(-6)^2+2(-6)+11$

$y=\frac{1}{6}*36-12+11$

$y=1*6-12+11$

$y=6-12+11$

$y=5$

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