What is the equation of the parabola that has a vertex at (56, -2) and passes through point (53,-9) ?

1 Answer
Dec 27, 2015

y = -7/9 (x-56)^2 -2

Explanation:

The general form of the equation is

y = a(x-h)^2 + k

Given color(blue)(h = 56), color(green)(k = -2)

color(red)(x = 53) , color(purple)(y = -9)

Substitute into the general form of the parabola

color(purle)(-9) = a((color(red)(53)-color(blue)(56))^2 color(green)(-2)
-9 = a(-3)^2-2

-9 = 9a -2

Solve for a

-9 + 2 = 9a

-7 = 9a

-7/9= a

The equation for parabola with the given condition will be

graph{y= -7/9 (x-56)^2 -2 [-10, 10, -5, 5]}