Question

A parabola has the equation –5x2 + 30x – y – 34 = 0. Which equation is that of the parabola in vertex form?

A) y = –5(x – 3)2 + 11
B) y = –5(x + 3)2 – 11
C) y = –5(x + 3)2 + 11
D) y = –5(x – 3)2 – 11

Answer 1

We can complete the square to get a standard form quadratic into vertex form. First, add Y and 34 to the right side of the equation. You’ll get -5x^2 + 30x = y + 34.
Next, you need to factor out a -5 from the left side, so you’ll get -5(x^2 -6x) = y + 34. Then, complete the square on the left. You’ll get -5(x-3)^2 = y - 11. Finally, add 11. The answer is y = -5(x-3)^2 + 11