Download presentation

Presentation is loading. Please wait.

Published byLydia Wright Modified over 5 years ago

2
Warm-up 1. Solve the following quadratic equation by Completing the Square: x 2 - 10x + 15 = 0 2. Convert the following quadratic equation to vertex format y = 2x 2 – 8x + 20

3
Chapter 4 Section 4-8 The Discriminant

4
Objectives I can calculate the value of the discriminant to determine the number and types of solutions to a quadratic equation.

5
Quadratic Review Quadratic Equation in standard format: y = ax 2 + bx + c Solutions (roots) are where the graph crosses or touches the x-axis. Solutions can be real or imaginary

6
Types of Solutions

7
2 Real Solutions 1 Real Solution 2 Imaginary Solutions

9
Key Concept for this Section What happens when you square any number like below: x 2 = ? It is always POSITIVE!! This is always the biggest mistake in this section

10
Key Concept #2 What happens when you subtract a negative number like below: 3 - -4 = ? It becomes ADDITION!! This is 2 nd biggest error on this unit!

11
The Quadratic Formula The solutions of any quadratic equation in the format ax 2 + bx + c = 0, where a 0, are given by the following formula: x = The quadratic equation must be set equal to ZERO before using this formula!!

12
Discriminant The discriminant is just a part of the quadratic formula listed below: b 2 – 4ac The value of the discriminant determines the number and type of solutions.

13
Discriminant Possibilities Value of b 2 -4ac Discriminant is a Perfect Square? # of Solutions Type of Solutions > 0Yes2Rational > 0No2Irrational < 02Imaginary = 01Rational

14
Example 1 What are the nature of roots for the equation: x 2 – 8x + 16 = 0 a = 1, b = -8, c = 16 Discriminant: b 2 – 4ac (-8) 2 – 4(1)(16) 64 – 64 = 0 1 Rational Solution

15
Example 2 What are the nature of roots for the equation: x 2 – 5x - 50 = 0 a = 1, b = -5, c = -50 Discriminant: b 2 – 4ac (-5) 2 – 4(1)(-50) 25 – (-200) = 225, which is a perfect square 2 Rational Solutions

16
Example 3 What are the nature of roots for the equation: 2x 2 – 9x + 8 = 0 a = 2, b = -9, c = 8 Discriminant: b 2 – 4ac (-9) 2 – 4(2)(8) 81 – 64 = 17, which is not a perfect square 2 Irrational Solutions

17
Example 4 What are the nature of roots for the equation: 5x 2 + 42= 0 a = 5, b = 0, c = 42 Discriminant: b 2 – 4ac (0) 2 – 4(5)(42) 0 – 840 = -840 2 Imaginary Imaginary

18
GUIDED PRACTICE for Example 4 Find the discriminant of the quadratic equation and give the number and type of solutions of the equation. 4. 2x 2 + 4x – 4 = 0 SOLUTION Equation DiscriminantSolution(s) ax 2 + bx + c = 0b 2 – 4ac 2x 2 + 4x – 4 = 0 4 2 – 4(2)(– 4 ) x = – b+ b 2 – 4ac 2ac = 48 Two irrational solutions

19
GUIDED PRACTICE for Example 4 5. SOLUTION Equation DiscriminantSolution(s) ax 2 + bx + c = 0b 2 – 4ac 12 2 – 4(12)(3 ) x = – b+ b 2 – 4ac 2ac = 0 One rational solution 3x 2 + 12x + 12 = 0

20
6. SOLUTION Equation DiscriminantSolution(s) ax 2 + bx + c = 0b 2 – 4ac x = – b+ b 2 – 4ac 2ac GUIDED PRACTICE for Example 4 8x 2 = 9x – 11 8x 2 – 9x + 11 = 0(– 9) 2 – 4(8)(11 ) = – 271 Two imaginary solutions

21
7. SOLUTION Equation DiscriminantSolution(s) ax 2 + bx + c = 0b 2 – 4ac x = – b+ b 2 – 4ac 2ac GUIDED PRACTICE for Example 4 7x 2 – 2x = 5 (– 2) 2 – 4(7)(– 5 ) = 144 Two rational solutions 7x 2 – 2x – 5 = 0

22
Homework WS 7-2

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google