# How do you write the equation of the parabola in vertex form given the vertex (9,-2) and point (12,16)?

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The equation of a parabola in vertex form is ( y = a(x - h)^2 + k ), where ( (h, k) ) is the vertex. Given the vertex ( (9, -2) ) and a point ( (12, 16) ), substitute these values into the equation to find ( a ). Then, rewrite the equation with the values of ( a ), ( h ), and ( k ).

- Using the vertex ( (9, -2) ) and the point ( (12, 16) ), determine the value of ( a ) using the point ( (12, 16) ):

[ 16 = a(12 - 9)^2 - 2 ]

- Simplify and solve for ( a ):

[ 16 = a(3)^2 - 2 ] [ 16 = 9a - 2 ] [ 18 = 9a ] [ a = 2 ]

- Substitute the values of ( a ), ( h ), and ( k ) into the vertex form of the parabola:

[ y = 2(x - 9)^2 - 2 ]

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