Problem

Given the vertex of a parabola is at the point (2,3) and the parabola passes through the point (1,-1), find the equation of the parabola.

Answer

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Answer

Step 4: Substitute a=-4 back into the equation to get the equation of the parabola: \(y=-4(x-2)^2 + 3\).

Steps

Step 1 ：Step 1: Remember the vertex form of a parabola's equation is \(y=a(x-h)^2 + k\), where (h, k) is the vertex of the parabola.

Step 2 ：Step 2: Substitute the vertex (2,3) into the equation to get \(y=a(x-2)^2 + 3\).

Step 3 ：Step 3: Substitute the point (1,-1) into the equation to find the value of a. \(-1=a(1-2)^2 + 3\), which simplifies to \(-1=a + 3\) and then to \(a=-4\).

Step 4 ：Step 4: Substitute a=-4 back into the equation to get the equation of the parabola: \(y=-4(x-2)^2 + 3\).

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