Rewrite the following equation of a parabola in standard for

Rewrite the following equation of a parabola in standard form y = - 4x^2 - 20x - 6 Additionally, state the coordinates of the vertex, x-intercepts (if any), and y-intercept.

Solution

Given equation is   y = -4x^2 – 20x – 6

1) Rewrite the equation with the x^2 and x terms (or the y^2 and y terms) on one side of the equation and the rest of the terms on the other side.

     4x^2 + 20x = -y – 6

2) Add a number to each side to make the side with the squared term into a perfect square trinomial (thus completing the square).

    4x^2 + 20x + 25 = -y – 6 + 25 ===========>     4x^2 + 20x + 25 = -y + 19

3) Rewrite the perfect square trinomial in factored form, and factor the terms on the other side by the coefficient of the variable.

(2x + 5)^2 = -(y - 19)

You now have the equation in standard form.

Vertex =========> (-5/2, 19)

x-intercept ========> (-4.679449, 0); (-0.320551, 0)