Quadratic Form to Vertex Form (please help!)?

Question

Please Help!! I have a project for Pre-calc and I'm trying to figure out how to change this equation (quadratic form) :
y = -4.97 x^2 + 10.91x + -5.16
into vertex form. I'm having a lot of trouble and I'm getting so confused.. Any help would be greatly appreciated!!

Thanks

Answer 1

You have an equation in the form of y = ax^2 + bx + c, and you want the form (y - k) = a(x - h)^2
Manipulating all those decimals can be very confusing, so let's try manipulating letters, instead.
a = -4.97
b + 10.91
c = -5.16
y = a(x^2 + (b/a)x) + c
y = a(x^2 + (b/a)x + (b/2a)^2x^2 - (b/2a)^2) + c
y = a(x^2 + (b/a)x + (b/2a)^2x^2) - a(b/2a)^2 + c
y + a(b/2a)^2 - c = a(2 + (b/2a))^2
y + (b^2/4a) - c = a(x + (b/2a))^2
(y + (b^2 - 4ac)/4a) = a(x + (b/2a))^2
Now, substituting the numbers back in:
(y +((10.91)^2 -4(-4.97)(-5.16))/(4(-4.97) = -4.97(x + (10.91/(2(-4.97))^2
(y + (119.0281 - 102.5808)/-19.88) = -4.97(x + (10.91/-9.94))^2
(y -16.4473/19.88) = -4.97(x - (10.91/9.94))^2
(y - 0.82733) ≈ -4.97(x - 1.0976)^2

Answer 2

put it in the form
y-k=a(x-h)^2
that will be the vertex form the vertices being
(h,k)
edit
the vertices are 1.1and 0.83