Question

How do you find the vertex of a parabola `y=x^2 - 9x`?

Answer 1

The vertex is at `color(red)((9/2,-81/4)`.

Explanation:

`y = x^2-9x`

The standard form of the equation for a parabola is

`y = ax^2+bx+c`, so

`a = 1`, `b = -9`, `c = 0`

The `x`-coordinate is at `x = -b/(2a) = -(-9)/(2×1) = 9/2`

To find the `y`-coordinate of the vertex, substitute `x =9/2` into the equation to get

`y = (9/2)^2 – 9(9/2) = 81/4 – 81/2 = 81/4 – 162/4 = -81/4`

The vertex is at (`9/2,-81/4`).

graph{y = x^2-9x [-10, 20, -25, 25]}

Answer 2

Another way of graphing can be as explained below.

Explanation:

After writing the quadratic equation in vertex form y= `(x-9/2)^2 -81/4`, graphing can be done by translating the graph of y=`x^2`, first horizontal shift to the right by `9/2` units and then vertical shift down wards by `-81/4` units