this question is confusing me

Question

Determine the values of a and b in relation y = ax^2 + bx – 157 if the vertex is located at (– 6, – 13)

I know I have to find the axis of symmetry but I'm not 100% sure how to without a or b. Can someone help me please?

Answer 1

I have a different approach to this problem. We know that the vertex is at -b/2a so

-6=-b/2a -12a=-b b=12a We will substitute this for b in the original equation so we will just have one unknown a to solve for

y= ax^2 +12(ax) -157. Use the point (-6,-13) for your x and y values

-13 = a(-6)^2+ 12(-6)a -157

144= 36a -72a

a=-4 Since b=12a b=-48 so equation is

Y = -4x^2 -48x -157

If you graph this equation you will see that the vertex indeed is at (-6,-13)

Answer 2

From the vertex form, you know that the parabola can be written a (y+13) = c(x+6)². You also know from the reqular form that x = 0 leads to y = -157.

Solve for c by plugging in (0, -157), multiply out the parts and rearrange into the form ax^2 + bx -157 = 0 and pick off the a and b values.

Good luck!