# solving equations algebraically

#### kevinryans1

##### New member
I have a problem with the question:

Find algebraically the equation of the axis of symmetry and the coordinates of the vertex of the parabola whose equation is y=-2x - 8x + 3.

I do not understand how to solve it algebraically. It would be great if you can help. Please and Thank You.

#### arthur ohlsten

##### Full Member
the equation as written is not a parabola. I assume you meant:
y=-2x^2-8x+3
we want the equation in the form
y=p[x-a]^2+b parabola open up if p is + open down if p=- vertex at a,b

y=-2x^2-8x+3 factor out -2 from first two terms
y=-2[x^2+4x] +3 complete the square
y=-2[x^2+4x+4]+8+3
y=-2[x+2]^2 + 11 answer

Arthur

#### Subhotosh Khan

##### Super Moderator
Staff member
kevinryans1 said:
I have a problem with the question:

Find algebraically the equation of the axis of symmetry and the coordinates of the vertex of the parabola whose equation is y=-2x - 8x + 3.

I do not understand how to solve it algebraically. It would be great if you can help. Please and Thank You.
The axis of symmetry is the vertical line through the vertex.

From the equation above, provided by Arthur, you can find the vertex and the axis of symmetry.

Let us know if you are still stuck.