[PDF] 8 7 skills practice solving quadratic systems

Overview

1.Explore the graphs of linear and quadratic systems

What are linear and quadratic systems, and how frequently do they appear on the test?

Linear and quadratic systems are systems of equations with one linear equation and one quadratic equation.

Quadratic systems: a line and a parabola

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Identifying solutions to linear and quadratic systems from graphs

A linear and quadratic system can be represented by a line and a parabola in the xyxyxyx, y-plane. Each intersection of the line and the parabola represents a solution to the system.

Try it!

TRY: determine the number solutions graphically

Quadratic system with no solutions

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Solving linear and quadratic systems algebraically

Our goal when solving a system of equations is to reduce two equations with two variables down to a single equation with one variable. Since each equation in the system has two variables, one way to reduce the number of variables in an equation is to substitute an expression for a variable.

Your turn!

Practice: identify solutions from a graph

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How do you solve a system of linear and quadratic equations?

In this lesson, you will study systems of linear and quadratic equations.This type of system can have one solution, two solutions, or no solutions. Solve the following system by graphing. Graph both equations on the same coordinate plane. Identify the point(s) of intersection, if any. 3, 4) and (1, 0) are the solutions of the system.

What will the students learn about quadratic functions?

Students will become aware of and appreciate the many uses and applications of quadratic functions. 2. Students will recognize the value of graphing calculators in exploring quadratic functions. 1. (Knowledge and Skill) Students will be albe to factor a simple quadratic equation to find intercepts.

How to solve quadratic programming problems?

One of the methods known to solve quadratic programming problems is Wolfe’s algorithm. This method is the simplest and the most easy to implement in a computer program. It can also be used to solve large class of quadratic programming problems .

How many solutions can a system of linear equations have?

A system of linear equations can have either one solution, no solutions, or infinitely many solutions. In Chapter 10, you solved quadratic equations graphically and algebraically. In this lesson, you will study systems of linear and quadratic equations.This type of system can have one solution, two solutions, or no solutions.

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