Parabola - Vertex, Intercepts
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(1) Write an equation for the parabola with vertex at (4,0) and y-intercept at (0,4). How many x-intercepts does the graph have?
(2) Find the equation for a parabola that has a vertex at (-12,-40) and passes through the point (6,68).
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(1) Let the parabola equation be y = ax^2 + bx + c. This contains the point (0, 4)
4 = c. The parabola is then y = ax^2 + bx + 4. The vertex of this parabola is given by
[-b/2a. (4ac ?b^2)/4a] = (4, 0)
-b/2a = 4, or ...
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