What are the vertex and the axis of symmetry of the equation y=2x^2+4x-10 please help and show work!!

Question

mathmale · Answer

y=2x^2+4x-10  is a quadratic function and has a graph which is a parabola.

The coefficients of the x-terms are, in order, 2, 4 and -10.

Rewrite this function in "vertex form," $$y=a(x-h)^2+k$$, to obtain the coordinates of the vertex:  they are (h, k).

From the quadratic formula, $$x=\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a },$$

mathmale · Answer

we get $$x=-b/(2a) $$

mathmale · Answer

as the equation of the axis of symmetry.

Please show your work, so that someone can give you feedback on what you've already done.

amanda0618 · Answer

what?
I'm so confused

jim_thompson5910 · Answer

@Amanda0618 do you see how `y=2x^2+4x-10 ` is in the form $\Large y = ax^2+bx+c$?

jim_thompson5910 · Answer

you may have to write it as y = 2x^2+4x+(-10)

mathmale · Answer

Compare YOUR quadratic equation with the standard form given you by Jim.
Determine through this comparison the values of the coefficients a, b and c.

Try finding the equation of the axis of symmetry first.  As before, it's x = -b/(2a).

mathmale · Answer

You have begun with the quadratic equation y = 2x^2+4x+(-10).  To find the coordinates of the vertex of the parabolic graph of this function, start by factoring out the coefficient 2:    y = 2(x^2 + 2x - 5).

You'll need to use the "completing the square" approach to rewrite  x^2 + 2x - 5 in the form    y = x^2 + 2x + 1 - 1 - 5.  Have you used this approach before?  If not, I'd suggest you look up "completing the square" and apply what you learn to rewriting x^2 + 2x - 5.

mathmale · Answer

Here's an example of "completing the square:"

Given y = x^2 - 6x + 2, rewrite this in the form y = x^2 - 6x + 9 - 9 + 2, or
y = x^2 - 6x + 9 + (-9 + 2).  Why?  Because x^2 - 6x + 9 is a perfect square.  This simplifies to 

y = (x-3)^2 - 7.  The vertex is (3, -7).

mathmale · Answer

I am trying to get you involved.  Please do and then share any work you can do on your own; then I could give you some meaningful feedback.  Once again:  quadratic equations come in several different forms, all of which you will likely need to learn.

y = a(x-h)^2 + k (vertex form)

y = 4px^2 (where p is the distance between focus and vertex)

y = ax^2 + bx + c ("standard form")

mathmale · Answer

Welcome to Open Study.

I know you're new and are likely exploring what others are typing in.

If you want help with a problem of your own, it's best to stick with it for a while, in case someone tries to help you.  After five or ten minutes of waiting for a reply from you, I'm ready to move on to helping others.