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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