Help with forming an equation of a parabola

Question

The vertex of a parabola is (-2, -20), and its y-intercept is (0, -12).

 

 equation of the parabola is y = ____x² + ____x + ____.

Answer 1

The equation of a parabola in vertex form is

 

y = a(x - h)² + k

 

where:

a is the coefficient of x² term

 

the vertex has coordinates  (h, k)

 

 

Since our vertex is (-2, -20), the equation will be

 

y = a(x + 2)² - 20

 

 

Now we solve for a using the y-intercept.

 

-12 = a(0 + 2)² - 20

 

-12 = 4a - 20

 

8 = 4a

 

2 = a

 

 

Plug this value of a into the vertex form of equation.

 

y = 2(x + 2)² - 20

 

 

Expand this vertex form so that it is in standard form.

 

y = 2(x² + 4x + 4) - 20

 

y = 2x² + 8x + 8 - 20

 

y = 2x² + 8x - 12