4.8 Use the Quadratic Formula and the Discriminant General Equation Quadratic Formula.
Solve quadratic equations using the Quadratic Formula. Classify roots using the discriminant.
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Transcript of Solve quadratic equations using the Quadratic Formula. Classify roots using the discriminant.
![Page 1: Solve quadratic equations using the Quadratic Formula. Classify roots using the discriminant.](https://reader031.fdocuments.net/reader031/viewer/2022031915/568132a8550346895d994ae9/html5/thumbnails/1.jpg)
Holt McDougal Algebra 2
5-6 The Quadratic Formula
Solve quadratic equations using the Quadratic Formula.
Classify roots using the discriminant.
Objectives
![Page 2: Solve quadratic equations using the Quadratic Formula. Classify roots using the discriminant.](https://reader031.fdocuments.net/reader031/viewer/2022031915/568132a8550346895d994ae9/html5/thumbnails/2.jpg)
Holt McDougal Algebra 2
5-6 The Quadratic Formula
discriminant
Vocabulary
![Page 3: Solve quadratic equations using the Quadratic Formula. Classify roots using the discriminant.](https://reader031.fdocuments.net/reader031/viewer/2022031915/568132a8550346895d994ae9/html5/thumbnails/3.jpg)
Holt McDougal Algebra 2
5-6 The Quadratic Formula
You can use the Quadratic Formula to solve any quadratic equation that is written in standard form, including equations with real solutions or complex solutions.
![Page 4: Solve quadratic equations using the Quadratic Formula. Classify roots using the discriminant.](https://reader031.fdocuments.net/reader031/viewer/2022031915/568132a8550346895d994ae9/html5/thumbnails/4.jpg)
Holt McDougal Algebra 2
5-6 The Quadratic Formula
Find the zeros of f(x)= 2x2 – 16x + 27 using the Quadratic Formula.
Example 1: Quadratic Functions with Real Zeros
Set f(x) = 0.
Write the Quadratic Formula.
Substitute 2 for a, –16 for b, and 27 for c.
Simplify.
Write in simplest form.
2x2 – 16x + 27 = 0
![Page 5: Solve quadratic equations using the Quadratic Formula. Classify roots using the discriminant.](https://reader031.fdocuments.net/reader031/viewer/2022031915/568132a8550346895d994ae9/html5/thumbnails/5.jpg)
Holt McDougal Algebra 2
5-6 The Quadratic Formula
Find the zeros of f(x) = x2 + 3x – 7 using the Quadratic Formula.
Set f(x) = 0.
Write the Quadratic Formula.
Substitute 1 for a, 3 for b, and –7 for c.
Simplify.
Write in simplest form.
Check It Out! Example 1a
x2 + 3x – 7 = 0
![Page 6: Solve quadratic equations using the Quadratic Formula. Classify roots using the discriminant.](https://reader031.fdocuments.net/reader031/viewer/2022031915/568132a8550346895d994ae9/html5/thumbnails/6.jpg)
Holt McDougal Algebra 2
5-6 The Quadratic Formula
Find the zeros of f(x)= x2 – 8x + 10 using the Quadratic Formula.
Set f(x) = 0.
Write the Quadratic Formula.
Substitute 1 for a, –8 for b, and 10 for c.
Simplify.
Write in simplest form.
Check It Out! Example 1b
x2 – 8x + 10 = 0
![Page 7: Solve quadratic equations using the Quadratic Formula. Classify roots using the discriminant.](https://reader031.fdocuments.net/reader031/viewer/2022031915/568132a8550346895d994ae9/html5/thumbnails/7.jpg)
Holt McDougal Algebra 2
5-6 The Quadratic Formula
The discriminant is part of the Quadratic Formula that you can use to determine the number of real roots of a quadratic equation.
![Page 8: Solve quadratic equations using the Quadratic Formula. Classify roots using the discriminant.](https://reader031.fdocuments.net/reader031/viewer/2022031915/568132a8550346895d994ae9/html5/thumbnails/8.jpg)
Holt McDougal Algebra 2
5-6 The Quadratic Formula
Make sure the equation is in standard form before you evaluate the discriminant, b2 – 4ac.
Caution!
![Page 9: Solve quadratic equations using the Quadratic Formula. Classify roots using the discriminant.](https://reader031.fdocuments.net/reader031/viewer/2022031915/568132a8550346895d994ae9/html5/thumbnails/9.jpg)
Holt McDougal Algebra 2
5-6 The Quadratic Formula
Find the type and number of solutions for the equation.
Example 3A: Analyzing Quadratic Equations by Using the Discriminant
x2 + 36 = 12x
x2 – 12x + 36 = 0
b2 – 4ac
(–12)2 – 4(1)(36)
144 – 144 = 0
b2 – 4ac = 0
The equation has one distinct real solution.
![Page 10: Solve quadratic equations using the Quadratic Formula. Classify roots using the discriminant.](https://reader031.fdocuments.net/reader031/viewer/2022031915/568132a8550346895d994ae9/html5/thumbnails/10.jpg)
Holt McDougal Algebra 2
5-6 The Quadratic Formula
Find the type and number of solutions for the equation.
Example 3B: Analyzing Quadratic Equations by Using the Discriminant
x2 + 40 = 12x
x2 – 12x + 40 = 0
b2 – 4ac
(–12)2 – 4(1)(40)
144 – 160 = –16
b2 –4ac < 0
The equation has two distinct nonreal complex solutions.
![Page 11: Solve quadratic equations using the Quadratic Formula. Classify roots using the discriminant.](https://reader031.fdocuments.net/reader031/viewer/2022031915/568132a8550346895d994ae9/html5/thumbnails/11.jpg)
Holt McDougal Algebra 2
5-6 The Quadratic Formula
Find the type and number of solutions for the equation.
Example 3C: Analyzing Quadratic Equations by Using the Discriminant
x2 + 30 = 12x
x2 – 12x + 30 = 0
b2 – 4ac
(–12)2 – 4(1)(30)
144 – 120 = 24
b2 – 4ac > 0
The equation has two distinct real solutions.
![Page 12: Solve quadratic equations using the Quadratic Formula. Classify roots using the discriminant.](https://reader031.fdocuments.net/reader031/viewer/2022031915/568132a8550346895d994ae9/html5/thumbnails/12.jpg)
Holt McDougal Algebra 2
5-6 The Quadratic Formula
Lesson Quiz: Part IFind the zeros of each function by using the Quadratic Formula.
1. f(x) = 3x2 – 6x – 5
2. g(x) = 2x2 – 6x + 5
Find the type and member of solutions for each equation.
3. x2 – 14x + 50 4. x2 – 14x + 48
2 distinct nonreal complex
2 distinct real
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Holt McDougal Algebra 2
5-6 The Quadratic Formula
Lesson Quiz: Part II5. A pebble is tossed from the top of a cliff. The
pebble’s height is given by y(t) = –16t2 + 200, where t is the time in seconds. Its horizontal distance in feet from the base of the cliff is given by d(t) = 5t. How far will the pebble be from the base of the cliff when it hits the ground?
about 18 ft