Solving Quadratics Using the Quadratic Formula
February 01, 2010
Solving Quadratics Using the Quadratic Formula
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Jan 16­5:30 PM
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Solving Quadratics Using the Quadratic Formula
February 01, 2010
So....what is the quadratic formula?
A long time ago, in a country far, far away........there was a Hindu mathematician named Brahmagupta. This brave soul took the equation ax2 + bx + c = 0 and solved the equation for x.
This was a very long mathematical process. The result was the following formula (known as the quadratic formula).
­b ± √b2 ­ 4ac
x = 2a
Note: There were many other mathematicians that solved this equation as well.
Jan 16­5:45 PM
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Solving Quadratics Using the Quadratic Formula
February 01, 2010
Example #1: Use the quadratic equation to find the x­intercepts of the following equation.
x2 + 5x ­ 90 = 0
Step 1: Put the equation in standard form (all x's and numbers on one side).
Step 2: Define a, b, and c.
Step 3: Use the quadratic formula.
­b ± √b2 ­ 4ac
x = 2a
Jan 16­5:59 PM
3
Solving Quadratics Using the Quadratic Formula
February 01, 2010
Example #2: Use the quadratic equation to find the x­intercepts of the following equation.
6x2 ­ 13x = 19
Step 1: Put the equation in standard form (all x's and numbers on one side).
Step 2: Define a, b, and c.
Step 3: Use the quadratic formula.
­b ± √b2 ­ 4ac
x = 2a
Jan 16­5:59 PM
4
Solving Quadratics Using the Quadratic Formula
February 01, 2010
What if the number under the
square root is negative?
­ 8
There are no "real" solutions.
(In other words...
it won't cross the x­axis)
Nov 26­3:58 PM
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Solving Quadratics Using the Quadratic Formula
February 01, 2010
Example #3: Use the quadratic equation to find the x­intercepts of the following equation.
3x2 ­ 19x + 40 = 0
Step 1: Put the equation in standard form (all x's and numbers on one side).
Step 2: Define a, b, and c.
Step 3: Use the quadratic formula.
­b ± √b2 ­ 4ac
x = 2a
Jan 16­5:59 PM
6
Solving Quadratics Using the Quadratic Formula
February 01, 2010
A cliff diver in Acapulco, Mexico, jumps from about 17 meters above the water. His height (h) in meters from the water t seconds after he jumps is given by the function h = ­ 4.9t2 + 1.5t + 17. How long will it take for the diver to reach the water?
(Hint: Use the quadratic formula!)
Why is only one of the answers a valid solution? Draw a picture to model this.
Jan 16­6:06 PM
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Solving Quadratics Using the Quadratic Formula
February 01, 2010
Homework
Solving Quadratics Using the Quadratic Formula Jan 16­6:18 PM
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