The vertex of the parabola below is at the point (1, 3), and the point (2, 6) is on the parabola. What is the equation of the parabola?A.y = 3(x - 1)2 + 3B.y = 6(x - 1)2 + 3C.y = 3(x + 1)2 - 3D.x = 2(y - 3)2 + 1SUBMITarrow_backPREVIOUS
Question
The vertex of the parabola below is at the point (1, 3), and the point (2, 6) is on the parabola. What is the equation of the parabola?A.y = 3(x - 1)2 + 3B.y = 6(x - 1)2 + 3C.y = 3(x + 1)2 - 3D.x = 2(y - 3)2 + 1SUBMITarrow_backPREVIOUS
Solution
The equation of a parabola in vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
Given that the vertex of the parabola is at the point (1, 3), we can substitute h = 1 and k = 3 into the equation, giving us y = a(x - 1)² + 3.
We also know that the point (2, 6) lies on the parabola. We can substitute x = 2 and y = 6 into the equation to solve for a:
6 = a(2 - 1)² + 3 6 = a(1)² + 3 6 = a + 3 a = 6 - 3 a = 3
Substituting a = 3 back into the equation gives us y = 3(x - 1)² + 3, which corresponds to option A.
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