Equation of the axis of symmetry for a parabola? [Solved!]

X

What is the equation of the axis of symmetry for a parabola?

Relevant page

<a href="/quadratic-equations/4-graph-quadratic-function.php">4. The Graph of the Quadratic Function</a>

What I've done so far

I couldn't find it anywhere.

X

Hi Sharon

The axis of symmetry of a parabola passes through the vertex (pointy bit) of the parabola and it divides the parabola exactly in half.

For the simple parabola 

`y = x^2`,

the axis of symmetry is the y-axis (whose equation is `x = 0`).

See the examples on this page: <a href="/quadratic-equations/4-graph-quadratic-function.php">4. The Graph of the Quadratic Function</a>

The first one has axis of symmetry `x = -1` It looks like this:

[graph]310,250;-5.3,5.3;-4.3,10.3,1,2;x^2+2x-3[/graph]

The second has axis of symmetry `x = 1.25`

[graph]310,250;-5.3,5.3;-4.3,10.3,1,2;-2x^2+5x+3[/graph]

You can work it out using the formula for the vertex given: 

`x = -\frac{b}{2a}`

Hope that helps.

X

But what about if its `x=y^2+2y+3`? There's no `x^2` now.

X

This is a parabola on its "side".

[graph]310,250;-3.3,5.3;-4.3,3;1,2;y^2+2y+3[/graph]

In this case, we'll have `a=1`, `b=2` and `c=3`. So what will the axis of symmetry be?

X

It's `y=-b/(2a) = -2/2 = -1`.

X

Yes, you are correct.