Question #c85cb

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1 Answer
sente
Nov 22, 2016

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

Explanation:

#y = a(x-p)^2+q# is the vertex form of a quadratic equation with vertex #(p, q)# As we are given the vertex as #(4, 3)#, we have #(p, q) = (4, 3)#. Substituting these in, we can write the equation as

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

As the graph passes through the point #(1, -15)#, we have

#-15 = a(1-4)^2+3#

#=> -15 = a(-3)^2+3#

#=> -15 = 9a+3#

#=> -18 = 9a#

#:. a = -2#

Thus the vertex form of the given quadratic is

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

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