Factored Form: y = a(x − r1)(x − r2)

  • a: determines whether the parabola opens up or down and how steep the curve is

  • r1 and r2: roots, x-intercepts

Match each definition below to the graph it describes.

y = 2(x - 1)(x + 5)

1

A

a parabola that opens down, with roots at 1 and 5 and a vertex at (3,12).

y = (x + 3)(x + 4)

2

B

a parabola that opens down, with roots at -3 and 4 and a vertex at (0.5,12.25).

y = - 3(x - 1)(x - 5)

3

C

a parabola that opens up, with roots at -3 and -4 and a vertex at (0.5, 5.125).

$$\displaystyle y = \frac{1}{2}(x + 3)(x - 4)$$

4

D

a parabola that opens up, with roots at 1 and -5 and a vertex at (-2,18).

y = - (x - 5)(x + 3)

5

E

a parabola that opens up, with roots at -3 and -3 and a vertex at (-3.5, -0.5).

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