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write the equation of the parabola that has a vertex at point (2,7) and passes through the point (-1,3)

y = (-4/9)x2 + (16/9)x + (47/9)

Step-by-step explanation:

f(x) = a(x - h)2 + k, where the vertex is (h,k) = (2,7) while passing through the point (x,y) = (-1,3). We must plug everything in to solve for a first. Then,

3 = a(-1 - 2)2 + 7

3 = a(-3)2 + 7Subtract 7 to both sides such that

-4 = 9aThen divide 9 such that

a = (-4/9)

Now we plug a into the equation with the vertex to create the parabolic function such that

y = (-4/9)(x - 2)2 + 7 Then FOIL the (x-2)2 such that

y = (-4/9)(x2 - 4x + 4) + 7Then distribute the (-4/9) inside such that

y = (-4/9)x2 + (16/9)x - (16/9) + 7Then (-16/9) + 7 = (-16/9) + (63/9) = 47/9

so,   y = (-4/9)x2 + (16/9)x + (47/9)

stethere all not eveanp-by-step explanation: