Curriculum  /  Math  /  9th Grade  /  Unit 7: Quadratic Functions and Solutions  /  Lesson 12

Quadratic Functions and Solutions

Lesson 12

Math

Unit 7

9th Grade

Lesson 12 of 13

Objective

Graph quadratic functions using $${x-}$$intercepts and vertex.

Common Core Standards

Core Standards

  • A.APR.B.3 — Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
  • F.IF.B.4 — For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
  • F.IF.C.7.A — Graph linear and quadratic functions and show intercepts, maxima, and minima.
  • F.IF.C.8.A — Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Criteria for Success

  • Understand the symmetry of a quadratic function. 
  • Understand the $${{{x-}}}$$coordinate of the vertex is exactly between the $${{{x-}}}$$intercepts of the parabola; use this information to determine the coordinates of the vertex.
  • Find the coordinates of the vertex from the equation of a quadratic function in standard form. 
  • Graph quadratic functions by finding and using the $${{{x-}}}$$intercepts and vertex as three defining points of the parabola.

Tips for Teachers

In the upcoming Unit 8, students will learn the vertex form of a quadratic equation. In this lesson, they determine the vertex by using the formula $${x=-{b\over{2a}}}$$ and then substituting the value for $$x$$ into the equation to determine the value of the $${y-}$$coordinate.

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Anchor Problems

25-30 minutes

Problem 1

Use the quadratic equation below to answer the questions that follow.

$${y=x^2+2{x-}8 }$$

  1. Find the roots and then plot them on a coordinate plane.
  2. What equation represents the line of symmetry for this parabola?
  3. What is the $${x-}$$coordinate of the vertex of the parabola?
  4. What is the $${y-}$$coordinate of the vertex of the parabola?
  5. Sketch the parabola in the coordinate plane.

Guiding Questions

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Problem 2

The $${x-}$$coordinate of the vertex can be found from the standard form of a quadratic equation using the formula $${x=-{b\over2a}}$$.

Find the roots and vertex of the quadratic equation below and use them to sketch a graph of the equation. 

$$y=-3x^2+24{x-}36$$

Guiding Questions

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Problem 3

Use the coordinate plane below to answer the questions that follow.

a.  Write a quadratic equation that has the two points shown as solutions. 

b.  Find the vertex of the equation you wrote and then sketch the graph of the parabola. 

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

Sketch a graph of the function below using the roots and the vertex. 

$${f(x)=x^2+8x-20}$$

References

EngageNY Mathematics Algebra I > Module 4 > Topic A > Lesson 9 — Exit Ticket

Algebra I > Module 4 > Topic A > Lesson 9 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.

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

Interpret quadratic solutions in context.

Lesson 13
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Lesson Map

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

Topic A: Features of Quadratic Functions

Topic B: Factoring and Solutions of Quadratic Equations

Topic C: Interpreting Solutions of Quadratic Functions in Context

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