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]}