How do you write the equation of the parabola in vertex form given vertex (-4,-7) and also passes the point (-3,-4)?

1 Answer
Jan 31, 2017

There are 2 equations, one of the form, #y=a(x - h)^2+k#, and the other of the form, #x=a(y-k)^2+h#. Where #(h,k)# is the vertex and you solve for "a" using the given point.

Explanation:

Given the vertex #(-4,-7)# and passes through the point #(-3,-4)#

Using the first form:

#y = a(x- -4)^2 -7#

Substitute -3 for x and -4 for y:

#-4 = a(-3- -4)^2 -7#

#3 = a(1)^2#

#a = 3#

The first equation is:

#y = 3(x- -4)^2 - 7#

Here is the graph of the equation and the two points:

Desmos.com

Using the second form:

#x = a(y- -7)^2-4#

Substitute -3 for x and -4 for y:

#-3 = a(-4- -7)^2 -4#

#1 = a(3)^2#

#a = 1/9#

The second equation is:

#x = 1/9(y- -7)^2 - 4#

Here is the graph of the equation and the two points:

Desmos.com