If the equation (y = ax^2 + bx + c) is a parabola, find the quadratic constant of variation if the vertex of the parabola is at (2, -3) and it passes through the point (4, 5).

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Step:1 ：Step 1: Since the vertex form of a parabola is given by (y = a(x - h)^2 + k), where (h, k) is the vertex of the parabola, we can write the equation as (y = a(x - 2)^2 - 3).Step:2 ：Step 2: Substitute the point (4, 5) into the equation to solve for &#x27;a&#x27;. So, (5 = a(4 - 2)^2 - 3 Rightarrow 5 = 4a - 3).Step:3 ：Step 3: Solve the equation for &#x27;a&#x27;. Add 3 to both sides, then divide by 4 to isolate &#x27;a&#x27;. So, (a = (5 + 3) / 4 = 2).

Answer

Step: 1 ：Step 1: Since the vertex form of a parabola is given by (y = a(x - h)^2 + k), where (h, k) is the vertex of the parabola, we can write the equation as (y = a(x - 2)^2 - 3).Step: 2 ：Step 2: Substitute the point (4, 5) into the equation to solve for &#x27;a&#x27;. So, (5 = a(4 - 2)^2 - 3 Rightarrow 5 = 4a - 3).Step: 3 ：Step 3: Solve the equation for &#x27;a&#x27;. Add 3 to both sides, then divide by 4 to isolate &#x27;a&#x27;. So, (a = (5 + 3) / 4 = 2).

If the equation \(y = ax^2 + bx + c\) is a parabola, find the quadratic constant of variation if the vertex of the parabola is at (2, -3) and it passes through the point (4, 5).

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