Write quadratic equation in general form. Please explain where I went wrong.

Question

I can not provide an image but it is a parabola on a graph. The vertex is -3.5,-4 . The Left bound is -7,20 and the y-intercept on the right side is 20. I have to determine the equation for the quadratic function and write it in a general form. Here is what I have done.

Vertex= -3.5, -4 h= -3.5 x=-7

Left Bound= -7, 20 k= 4 y=20

Y= a(x-h)^2+k

20=a(-7-(-3.5)^2+4

20=a(-3.5)^2+4

20=a(-12.25)+4

-4 -4

16=a(-12.25)

and now I am lost. Thank you for your time.

Answer 1

a=16/12.25 = -64/49

y=(64/49)(x+3.5)^2 + 4 is the quadratic, parabolic curve, with vertex (3.5,4)

20=(64/49)3.5^2 + 4 = 64(49)(12.25) + 4 = 16+4

You made a slight arithmetic mistake when you went from

line 20=a(-3.5)^2 +4 to 20= a(-12/25) +4. You should have

20=a(+12/25), just a sign error