Question

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?

Answer 1

Coordinates of vertex are `(2,5)`

Explanation:

As the equation is of the form of `y=ax^2+bx+c`, where `a` is positive, hence parabola has a minimum and is open upwards and symmetric axis is parallel to `y`-axis.

As points `(-1,41)` and `(5,41)`, 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=(5-1)/2=2` and abscissa of vertex is `2`. and ordinate is given by `4*2^2-16*2+21=16-32+21=5`.

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