Curriculum  /  Math  /  9th Grade  /  Unit 8: Quadratic Equations and Applications  /  Lesson 7

Quadratic Equations and Applications

Lesson 7

Math

Unit 8

9th Grade

Lesson 7 of 15

Objective

Determine the number of real roots of a quadratic function using the discriminant of the quadratic formula.

Common Core Standards

Core Standards

  • F.IF.C.7.A — Graph linear and quadratic functions and show intercepts, maxima, and minima.
  • A.REI.B.4.B — Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Foundational Standards

  • 8.EE.A.2

Criteria for Success

  1. Understand why the discriminant determines the number of real roots of a quadratic function. 
  2. Use the discriminant to determine if a quadratic function has 0, 1, or 2 real roots. 
  3. Identify whether a quadratic function shown in a graph has 0, 1, or 2 real roots and describe what this means about the discriminant of the function. 

Tips for Teachers

Students are not expected to define imaginary roots or to represent $${\sqrt{-1}}$$  as $$i$$. This will come in Algebra 2. 

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Anchor Problems

25-30 minutes

Problem 1

To the right is a graph of a quadratic function. 

  1. How many roots does this quadratic function have? Explain your reasoning. 
  2. The equation for the function is $${ f(x)=x^2+4x+5}$$. Find the roots using the quadratic formula. How does this support what you observed in the graph?

Guiding Questions

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Problem 2

Use the quadratic formula to find the roots for each equation below. 

a.  $${-2x^2+x+15=y}$$

b.  $${8x^2+6x+5=y}$$

c.  $${3x^2-6x+3=y}$$

Guiding Questions

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Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

Problem 1

How many zeros does the function $${f(x)=3x^2+6x+2}$$ have? Explain your resoning.

References

EngageNY Mathematics Algebra I > Module 4 > Topic B > Lesson 15 — Exit Ticket, Question #3

Algebra I > Module 4 > Topic B > Lesson 15 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Write the equation of a quadratic function with no real roots.

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Next

Graph quadratic functions from all three forms of a quadratic equation.

Lesson 8
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Deriving the Quadratic Formula

Topic B: Transformations and Applications

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