problems factoring: find vertex of 2x^2 + 2x - y = -3

[Jen123]

Question: Find the cordinates of the vertex and the equation of the axis of symmetry for the parabola with equation 2x^2 + 2x - y = -3

So far I got: I didn't get very far on this question because i am having problems factoring. In my book to get the coordinates and the equation of the axis of symmentry it say that you must rewrite the equation in the form (x-h)^2 = 4p(y-k). So I seperated my terms and that's where I'm stuck I have 2x^2 + 2x = y-3. but i dont kno how i would factor this out to get it in the above form could somone help thanks?!

 

[tkhunny]

Re: problems factoring

Who told you to "factor"? You should be "completing the square".

2x^2 + 2x - y = -3

Good.

2x^2 + 2x = y - 3

Distributive Property of Multiplication over Addition

2(x^2 + x) = y - 3

Completing the Square

2(x^2 + 1x + _____) = y - 3 + 2*(______)

(1/2)^2 = 1/4

2(x^2 + 1x + (1/4)) = y - 3 + 2*(1/4)

2(x + 1/2)^2 = y - 3 + 2*(1/4) = y - 3 + 1/2 = y - 5/2

Is it looking familiar, yet?

 

[Deleted member 4993]

Question: Find the cordinates of the vertex and the equation of the axis of symmetry for the parabola with equation 2x^2 + 2x - y = -3

So far I got: I didn't get very far on this question because i am having problems factoring. In my book to get the coordinates and the equation of the axis of symmentry it say that you must rewrite the equation in the form (x-h)^2 = 4p(y-k). So I seperated my terms and that's where I'm stuck I have 2x^2 + 2x = y-3. but i dont kno how i would factor this out to get it in the above form could somone help thanks?!

You could do it by factoring.

That will give you the two points where y=0.

Vertex and line of symmetry will be at the midpoint of those two roots.

However, in this case it won't work (easily) because the roots are "complex". So follow tkhunny's method.