# What is the equation of the parabola that has a vertex at # (4, 6) # and passes through point # (-7,-8) #?

##### 2 Answers

#### Explanation:

Known: The equation standard form is

Using the two points to give simultaneous equations

Known that

So

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In vertex form:

#y = -14/121 (x-4)^2 + 6#

In standard polynomial form:

#y =-14/121 x^2 + 112/121 x +502/121#

#### Explanation:

The equation of a parabola with vertical axis can be expressed in vertex form as:

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

where

In our example, the equation of the parabola can be written in the form:

#y = a(x - 4)^2 + 6#

from which we can deduce:

#a = (y-6)/(x-4)^2#

Since we want our parabola to pass through

#a = (-8-6)/(-7-4)^2 = -14/121#

So the equation of our parabola may be written:

#y = -14/121 (x-4)^2 + 6#

#=-14/121 x^2 + 112/121 x - 224/121 + 6#

#=-14/121 x^2 + 112/121 x +502/121#

graph{-14/121 x^2 + 112/121 x +502/121 [-20, 20, -10, 10]}