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

### My question

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

### Relevant page

4. The Graph of the Quadratic Function

### What I've done so far

I couldn't find it anywhere.

X

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

What I've done so far

I couldn't find it anywhere.

## Re: Equation of the axis of symmetry for a parabola?

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).

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

The second has axis of symmetry x = 1.25

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

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

Hope that helps.

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).

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.

## Re: Equation of the axis of symmetry for a parabola?

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

X

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

## Re: Equation of the axis of symmetry for a parabola?

This is a parabola on its "side".

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

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?

## Re: Equation of the axis of symmetry for a parabola?

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

X

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

## Re: Equation of the axis of symmetry for a parabola?

Yes, you are correct.

X

Yes, you are correct.