10-7 Using Factors to Sketch y = x 2 + bx + c notes
10-7 Using Factors to Sketch y = x 2 + bx + c notes
10-7 Using Factors to Sketch y = x 2 + bx + c notes
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Mrs. Aitken’s Integrated 1 Math<br />
Unit <strong>10</strong> Quadratic Equations as Models<br />
You can pick the order <strong>to</strong> guess and check…check using FOIL.<br />
<strong>Fac<strong>to</strong>rs</strong> of -6 Plug these in and use guess and check <strong>to</strong> figure out your answer.<br />
Use FOIL <strong>to</strong> check your answer<br />
-2 • 3 (x - 2) (x + 3) x 2 + 3x - 2x - 6 = x 2 + x - 6 nope<br />
-3 • 2 (x - 3) (x + 2) x 2 + 2x - 3x - 6 = x 2 - x - 6 YES<br />
-1 • 6 (x - 1) (x + 6) x 2 + 6x - x - 6 = x 2 + 5x - 6 nope<br />
-6 • 1 (x - 6) (x + 1) x 2 + x - 6x - 6 = x 2 - 5x - 6 nope<br />
(x – 3)(x + 2)<br />
Example 2:<br />
Fac<strong>to</strong>r x 2 + 7x – 18<br />
Solution<br />
c = -18<br />
b = 7<br />
You can pick the order <strong>to</strong> guess and check.<br />
<strong>Fac<strong>to</strong>rs</strong> of -18 Plug these in and use guess and check <strong>to</strong> figure out your answer.<br />
Use FOIL <strong>to</strong> check your answer<br />
-1 • 18 (x - 1) (x + 18) x 2 + 18x - x - 18 = x 2 + 17x - 18 nope<br />
-18 • 1 (x - 18) (x + 1) x 2 + x - 18x - 18 = x 2 - 17x - 18 nope<br />
-2 • 9 (x - 2) (x + 9) x 2 + 9x - 2x - 18 = x 2 +7x - 18 YES<br />
-9 • 2 (x - 9) (x + 2) x 2 + 2x - 9x - 18 = x 2 - 7x - 18 nope<br />
-3 • 6 (x - 3) (x + 6) x 2 + 6x - 3x - 18 = x 2 + 3x - 18 nope<br />
-6 • 3 (x - 6) (x + 3) x 2 + 3x - 6x - 18 = x 2 - 3x - 18 nope<br />
(x – 2)(x + 9)<br />
Side-note: Notice -2(9) = -18
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