Question #c85cb

1 Answer
sente
Nov 22, 2016

y = -2(x-4)^2+3y=−2(x−4)2+3

Explanation:

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

y = a(x-4)^2+3y=a(x−4)2+3

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

-15 = a(1-4)^2+3−15=a(1−4)2+3

=> -15 = a(-3)^2+3⇒−15=a(−3)2+3

=> -15 = 9a+3⇒−15=9a+3

=> -18 = 9a⇒−18=9a

:. a = -2

Thus the vertex form of the given quadratic is

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

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