#### A parabola opening up or down has vertex (2, 7) and passes through ( 4, 3). Write its equation in vertex form

Anonymous

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Sangeetha Pulapaka

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STEP 1: Recall what is a parabola

https://www.mathsisfun.com/geometry/parabola.html

STEP 2: Recall the standard form of a parabola in vertex form

https://www.qalaxia.com/viewDiscussion?messageId=5d1433777ae99744ef6d360d

The standard form of the equation of any parabola whose vertex is (h, k) is:

f(x)=a(x-h)^{2}+k

The vertex of this parabola is (2, 7)

f(x)=a(x-2)^{2}+7

STEP 3: Find the equation of the parabola that passes through the vertex and the point

This parabola goes through the point (4, 3) so plug in x=4 and f(x)=3

3=a(4-2)^{2}+7

,3=4a+7

-4=4a

-1=a

Therefore the equation of this parabola is:

F(x)=-(x-2)^2+7