How do you write a quadratic equation with vertex (-2,-3) and goes through the point (-4,25)?

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Answer 1 · 2018-07-02T05:58:40

#y = 7(x + 2)^2 - 3 " or "y = 7x^2 + 28x + 25#

Given: quadratic equation with vertex #(-2, -3)#, through #(-4, 25)#

Vertex form: #y = a(x-h)^2 + k#, where vertex #(h, k)# and #a# is a constant.

#y = a(x + 2)^2 - 3#

Solve for #a# using the point #(-4, 25)#:

#25 = a(-4 + 2)^2 - 3#

#25 = (-2)^2a - 3#

#25 = 4a - 3#

#28 = 4a#

#a = 28/4 = 7#

Equation: #y = 7(x + 2)^2 - 3#

To put it in general form:

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

#y = 7x^2 + 28x + 25#

graph{7(x + 2)^2 - 3 [-5, 5, -5, 25]} #