Lesson 1 of 13
The input that lands on zero
Show on a big screenA ball's height follows a rule: −5x² + 40x. Here x is the input and the height is the value. At some x, the height is 0.
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−5x² + 40x. Try x = 8. Step 1 of 4
- Rule:
−5x² + 40x. Tryx = 8. - First term:
−5 × 8² = −320. - Second term:
40 × 8 = 320. - Add them:
−320 + 320 = 0.
The rule
A zero is an input where a polynomial's value is 0. Use the input in place of x. Work out each term. Add them.
So 8 is a zero of −5x² + 40x. The value at 8 is 0. The word names the input, not the value 0.
| Polynomial | Try | Value | Zero? |
|---|---|---|---|
2x + 3 | 0 | 3 | no |
2x + 3 | −3/2 | 0 | yes |
x² − 5x + 6 | 2 | 0 | yes |
The ball also starts at height 0, at x = 0: −5×0² + 40×0 = 0. So −5x² + 40x has two zeros, 0 and 8. The ball leaves the ground at 0 and lands at 8.
A linear polynomial ax + b, with a not 0, has one zero, −b/a. Here a and b are fixed numbers. Solve ax + b = 0. Then ax = −b, so x = −b/a.
Try the lab to finish this lesson.