Question

What is the `x`-coordinate of the vertex of the parabola `y=x^2+6x`?

Answer 1

The x-coordinate value of the vertex is given by `color(blue)(-3`

Explanation:

Given:

`color(red)(y=x^2+6x`

We must find the x-coordinate value of the Vertex of the parabola.

For a parabola of the form `color(blue)(ax^2+bx+c`,

the x-coordinate value of the vertex is given by `color(blue)(-b/(2a)`

In `color(red)(y=x^2+6x`, we can see that `color(green)(a=1, and b = 6`.

When we use the formula, `color(blue)(-b/(2a)`, we get

`color(blue)(x=-(6)/(2*1))=-6/2 = -3`

Hence, the x-coordinate value of the vertex is given by `color(blue)(-3`

You can also examine the image of the graph below:

Hope it helps.