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5-55.

QUALITY CONTROL, Part Three

Lots O’Dough, a wealthy customer, would like to order a variety of parabolas. However, he is feeling pressed for time and says that he will pay you lots of extra money if you complete his order for him. Of course you agree! He sends you sketches of each parabola that he would like to receive. Determine a possible equation for each parabola so that you can pass this information on to the Function Factory.

  1. Sketch A is an upward parabola with x intercepts at (negative 4, comma 0) and (2, comma 0). The vertex is in the third quadrant.

    The -intercepts are a good place to find factors of the quadratic equation.

  1. Sketch B is an upward parabola with the vertex at (3, comma 0) and points at (4, comma 32), and (0, comma 0).

    There is only one -intercept, but this is a parabola, so the equation needs to be quadratic.

  1. Sketch C is an upward parabola with the vertex in the fourth quadrant and x intercepts at (0, comma 0) and (7, comma 0).

    Use the -intercepts to help you write a possible equation.

  1. Sketch D is a downward parabola with the vertex in the second quadrant.  The x intercepts are at (negative 5, comma 0) and (1, comma 0).

    Notice that this parabola opens downward.