alg ii unit 4-9 solving quadratic systems

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