Writing Quadratic Equations Using the Vertex Formula

Students learn to write quadratic equations in y - k = a(x - h)2 form using given information about the vertex of the parabola and a point on the parabola. For example, to write the equation of a parabola that has a vertex of (1, 7) and contains the point (4, 25), the first step is to substitute the coordinates of the vertex in for h and k in the formula, and substitute the coordinates of the point in for x and y in the formula. Next, solve the equation for a, then substitute the values of a, h, and k back into the original formula to write the equation of the parabola.

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