Warm UP

1
Warm UP

• Solve the following quadratic Inequality
• 5-2x2 -3x
• 4x2 lt 9

2
Unit 5 Quadratic Functions

• Section 11 Nonlinear systems

3
Essential Question

• What methods can you use to solve a system that
  includes a linear equation and a quadratic
  equation?

4
Standards in this sectionText book pages
P548-555

• MCC9-12.A.REI.7 Solve a simple system consisting
  of a linear equation and a quadratic equation in
  two variables algebraically and graphically.

5
Vocabulary

• Nonlinear system of equations- a system in which
  at least one of the equations is non linear.

6
A system made up of a linear equation and a
quadratic equation can have no solution, one
solution, or two solutions, as shown below.
7
Example 1 Solving a Nonlinear System by Graphing
Solve the system by graphing. Check your answer.
Step 1 Graph y x2 4x 3. The axis of
symmetry is x 2. The vertex is (2, 1). The
y-intercept is 3. Another point is (1, 0).
8
(No Transcript)
9
Example 2 Solving a Nonlinear system by
substitution.
Solve the system by substitution.
Both equations are solved for y, so substitute
one expression for y into the other equation for
y.
-3x 3 x2 x -5
Substitute -3x 3 for y in the first equation
10
Check It Out! Example 2
1. Solve the system by substitution. Check your
answer.
Both equations are solved for y, so substitute
one expression for y into the other equation for
y.
Subtract -3x 4 for y in first equation.
-3x 4 3x2 - 3x 1
0 3x2 - 3
Subtract -3x 4 from both sides
11
Example 3 Solving a Nonlinear System
A
12
Check It Out! Example 3
1. Solve each system by elimination. Check your
answers..
Write the system to align the y-terms
2x - y 2 y x2 - 5
Add to eliminate y
2x x2 - 3
-2x
-2x
Subtract 2x from booth sides
13
Example 4 Physics Application
The increasing enrollment at South Ridge High
School can be modeled by the equation E(t) -t2
25t 600, where t represents the number of
years after 2010. The increasing enrollment at
Alta Vista High School can be modeled by the
equation E(t) 24t 570. In what year will the
enrollments at the two schools be equal?
14
(No Transcript)
15
Examples
Solve each system.
(1, 0), (4, 3)
1.
(-1, 6), (4, -9)
2.
16
Examples
no solution
3.
(3, -2), (6, 4)
4.
17
Homework Text book (Exercises 16-4) P 552 1-9
Worksheets Nonlinear systems practice I, II,
and III Coach book p 236-237 1-9