Question 550954: write the equation of the parabola in vertex form: vertex (3,3) that goes through the point (-2,53).
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website! write the equation of the parabola in vertex form: vertex (3,3) that goes through the point (-2,53).
The standard form of a parabola is
y = a(x - h)² + k where the vertex is the point (h,k)
In this case (h,k) = (3,3), so the above becomes
y = a(x - 3)² + 3
Since is contains the point (x,y) = (-2,53)
53 = a(-2 - 3)² + 3
53 = a(-5)² + 3
53 = a(25) + 3
53 = 25a + 3
50 = 25a
2 = a
Substitute 2 for a in
y = a(x - 3)² + 3
y = 2(x - 3)² + 3
That's the equation you were looking for.
The graph is
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