QUADRATIC FUNCITONS

k_wood98

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Joined
Aug 6, 2005
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I am seriuously not understanding this and was hoping someone could help me out. :shock: I am working some quadratic equations and need to find the vertex and intercepts to sketch:

y = x² + 4x

x² - x – 20 ≤ 0

If someone could please explain this to me and help me out I would greatly appreciate it. Thanks in advance.
 
To find the x-intercepts, plug in zero for y and solve, using whatever method (such as the Quadratic Formula) that you like.

To find the vertex, just plug into the formula:

. . . . .h = -b/2a

For instance:

. . . . .y = 3x<sup>2</sup> - 4x + 1

. . . . .0 = 3x<sup>2</sup> - 4x + 1

. . . . .x = [4 ± sqrt(16 - 9)] / 6 = [4 ± sqrt(7)] / 6

. . . . .x-intercepts: x = 0.677, x = 3.323, approximately

. . . . .h = -(-4)/[2(3)] = 4/6 = 2/3

. . . . .k = 3(2/3)<sup>2</sup> - 4(2/3) + 1

. . . . . = 3(4/9) - 8/3 + 3/3 = 4/3 - 8/3 + 3/3 = -1/3

. . . . .(h, k) = (2/3, -1/3)

Follow this procedure with your exercise.

Eliz.
 
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