# Jen knows that (-1,41) and (5, 41) lie on a parabola defined by the equation #y=4x^2-16x+21. What are the coordinates of the vertex?

Nov 22, 2016

Coordinates of vertex are $\left(2 , 5\right)$

#### Explanation:

As the equation is of the form of $y = a {x}^{2} + b x + c$, where $a$ is positive, hence parabola has a minimum and is open upwards and symmetric axis is parallel to $y$-axis.

As points $\left(- 1 , 41\right)$ and $\left(5 , 41\right)$, both lie on parabola and their ordinate being equal, these are reflection of each other w.r.t. symmetric axis.

And hence symmetric axis is $x = \frac{5 - 1}{2} = 2$ and abscissa of vertex is $2$. and ordinate is given by $4 \cdot {2}^{2} - 16 \cdot 2 + 21 = 16 - 32 + 21 = 5$.

Hence coordinates of vertex are $\left(2 , 5\right)$ and parabola looks like
graph{y=4x^2-16x+21 [-10, 10, -10, 68.76]}