I need help with this problem.

Question

The equation of the parabola is -4y+8x^2=-32+48x write the equation in Vertex form but first's needs to be converted into standard form and simplify any fractions.

I'm doing IXL and I'm close to finishing please help me and tell what i did wrong if I did get it incorrect this is the answer I got please correct me if it's wrong: y=2(x-3)^2-10.

Answer 1

You might want to just divide by 4 to start to simplify the numbers

-y + 2x^2 = -8 + 12x

change the signs(same as dividing or multiplying by negative 1), and move the x^2 term to the right side (same as adding 2x^2 to both sides)

y-2x^2 =8 -12x

y = 2x^2 -12x +8

factor out 2 from the x terms

y = 2(x^2 -6x) + 8

complete the square, (same as adding 2(9) and subtracting 18)

y = 2(x^2 -6x +9) + 8-18

y = 2(x-3)^2 -10

You got it right.

vertex is (3,-10) as it's written in vertex form

y=a(x-h)^2 + k where (h,k) is the vertex (and the minimum point for an upward opening parabola)