Write the equation of a parabola in standard form with vertex (-2,3) that passes through f(2)=7

parabola equation: y=k(x-b)^2+h

b=x component of the vertex, in this case -2

h=y component of the vertex, in this case 3

so you get y=k(x-(-2))^2+3

now plug in f(2)=7, which is x=2, y=7, you get

7=k(2+2)^2+3, k=1/4

Thus, the equation of the parabola is y=(1/4)(x+2)^2+3

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