Solve systems of linear and quadratic functions algebraically

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Objective

SWBAT solve a system of linear and quadratic functions algebraically.

Big Idea

Use substitution and "making zeroes" to solve systems of linear and quadratic functions algebraically.

Lesson Author

Jeff Li MTP

New York, NY

Grade Level

Eighth grade

Subjects

Math

Systems of Equations and Inequalities

Algebra

Quadratic Equations

substitution method

Standards

HSA-REI.C.7

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x<sup>2</sup> + y<sup>2</sup> = 3.

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP6

Attend to precision.

MP7

Look for and make use of structure.

Warm-up

10 minutes

Each day, students complete a Warmup that usually consists of spiraling the previous day's material, in addition to older material. Warm-up problems also sometimes extend lessons that students have encountered before to more unfamiliar contexts.

Today's warm-up, because students differ so much in their speeds in finishing graphing tasks, has a bonus question for the early finishers to extend their knowledge. It's not necessary in my class for all kids to do the second problem.