What is the equation of the parabola that has a vertex at # (-12, 5) # and passes through point # (-3,-15) #?

1 Answer
Johnson Z.
Feb 1, 2016

equation: #y=-20/81(x+12)^2+5#

Explanation:

Recall that the general equation for a quadratic equation in vertex form is:

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

where:
#y=#y-coordinate
#a=#vertical stretch/compression
#x=#x-coordinate
#h=#horizontal translation or x-coordinate of vertex
#k=#vertical translation or y-coordinate of vertex

To find the equation of the parabola, substitute your known values into the equation to solve for the unknown variable:

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

#-15=a(-3-(-12))^2+5#

#-20=a(9)^2#

#-20=a(81)#

#a=-20/81#

#:.#, the equation of the parabola is #y=-20/81(x+12)^2+5#.

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