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28 votes
28 votes
Write the equation of the parabola in vertex form.vertex (3,1), point (2,-2)f(x) =

User George Leung
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1 Answer

16 votes
16 votes

rom the point it passed We were given

Vertex = (3,1)

Point = (2, -2)

The equation of the parabola is given by:


y=a(x-h)^2+k

where (h, k) is the vertex = (3,1)

a is a cnstant

On substitution:


y=a(x-3)^2+1

Substituting the value of (x,y) from the point it passed through to find a:


\begin{gathered} y=a(x-3)^(2)+1 \\ \\ -2=a(2-3)^2+1 \\ \\ -2=a+1 \\ \\ a=-3 \end{gathered}

Therefore substitute a into the original equation:


y=-3(x-3)^2+1

The equation of the parabola is given by:

y = -3(x-3)^2 + 1

User Libni
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