alg ii unit 4-9 solving quadratic systems
TRANSCRIPT
4-9 THE QUADRATIC SYSTEMSChapter 4 Quadratic Functions and Equations
©Tentinger
ESSENTIAL UNDERSTANDING AND OBJECTIVES
Essential Understanding: you can solve systems involving quadratic equations using methods similar to the ones used to solve systems of linear equations
Objectives: Students will be able to:
Solve and graph systems of linear and quadratic equations
Solve and graph systems of quadratic inequalities
IOWA CORE CURRICULUM
Algebra A.CED.3. Represent constraints by equations
or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context
A.REI.7* Solve a simple system consisting of a linear equation and quadratic equation in two variables algebraically and graphically
LINEAR-QUADRATIC SYSTEM
Solutions of Linear Quadratic System A system of one quadratic equation and one
linear equation can have two solutions, one solution, or no solution.
NEED PICTURES OF EACH
SOLVING A LINEAR-QUADRATIC SYSTEM BY GRAPHING
€
y = −x2 − x + 6
y = x + 6
⎧ ⎨ ⎩
€
y = x2 + 6x + 9
y = x + 3
⎧ ⎨ ⎩
€
y = x2 − 2x +1
y = x − 3
⎧ ⎨ ⎩
SOLVING A LINEAR-QUADRATIC SYSTEM BY SUBSTITUTION
€
y = −x2 − 3x +10
y = x + 5
⎧ ⎨ ⎩
€
y = −x2 + 3x + 9
y = −3x + 4
⎧ ⎨ ⎩
SOLVING A QUADRATIC SYSTEM OF EQUATIONS BY SUBSTITUTION
€
y = x2 + 9x + 7
y = −x2 + 3x + 7
⎧ ⎨ ⎩
€
y = x2 − 4x + 5
y = −x2 + 5
⎧ ⎨ ⎩
€
y = x2 − 4x + 5
y = −x2 − 5
⎧ ⎨ ⎩
SOLVING A QUADRATIC SYSTEM OF INEQUALITIES
€
y ≤ −x2 − 4x + 3
y > −x2 + 3
⎧ ⎨ ⎩
€
y ≥ x2 + 5x − 8
y < −x2 + 3x + 4
⎧ ⎨ ⎩
HOMEWORK
Pg. 262 – 263 #9 – 51 (3s), 53 - 55