The vertex of this parabola is at (2,-4). When the y-value is -3, the x-value -3. What is the coefficient of the squared term in the parabola's equation?

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Answer 1 · 2018-06-23T18:07:36

There are two parabolas that meet your specifications.

The first parabola is of the form:

#y = a_1(x-2)^2-4#

The second parabola is of the form:

#x = a_2(y- -4)^2+2#

Find the value of #a_1# by substituting #y(-3) = -3#:

#-3 = a_1(-3-2)^2-4#

#1 = a_1(-3-2)^2#

#a_1 = 1/25#

Find the value of #a_2# by substituting #x(-3) = -3#:

#-3 = a_2(-3- -4)^2+2#

#a_2 = -5#

The two equations that meet your requirements are:

#color(red)(y = 1/25(x-2)^2-4)# and #color(blue)(x = -5(y- -4)^2+2)#

Please observe that both parabolas have their vertex at #(2,-4)# and contain the point #(-3,-3)#:

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