math precalculus

Question

Write the equation of the parabola if: the vertex is (-2, -8), ad the point (-20, 12) is on the parabola

Answer 1

If the vertex is at (-2, -8) we can always write a parabola in vertex form using...

f(x) = a*(x - h)² + k

where a, h, and k are parameters we can fit to the points/curve we want. The vertex is defined from above at (h,k).

With the vertex information provided...

f(x) = a(x + 2)² - 8

Since we have a point on the parabola --> (-20,12). gives us an (x,y) we can use

12 = a(-20 + 2)² - 8

We can solve for a now and complete our definition of the parabola...

20 = a * (-18)² --> a = 20/324 = 5/81

f(x) = 5/81 * (x + 2)² - 8