Quadratic Equations and Applications

Lesson 8

Math

Unit 8

9th Grade

Lesson 8 of 15

Objective


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

Common Core Standards


Core Standards

  • F.IF.C.7.A — Graph linear and quadratic functions and show intercepts, maxima, and minima.

Foundational Standards

  • A.SSE.A.1
  • A.SSE.B.3.A

Criteria for Success


  1. Graph a quadratic function from standard form, identifying features of the parabola that can be determined immediately from its form.
  2. Graph a quadratic function from intercept form, identifying features of the parabola that can be determined immediately from its form. 
  3. Graph a quadratic function from vertex form, identifying features of the parabola that can be determined immediately from its form. 
  4. Compare features of parabolas given as equations in different forms.

Tips for Teachers


This lesson connects back to Lesson 5, where students compared and converted between the three forms of a quadratic equation. Having learned the quadratic formula in Lesson 6, students now have an additional strategy to find the roots from standard form. 

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Anchor Problems

25-30 minutes


Problem 1

A quadratic function is represented in three different equation forms. For each feature listed, either give the value that is revealed by the equation’s form or briefly explain how you would determine the value. 

Then use the information to graph the quadratic function.

  $${-(x-3)(x+5)=y}$$ $${-(x+1)^2+16=y}$$ $${-x^2-2x+15=7}$$
$${y-}$$intercept

 

 

   
roots

 

 

   
vertex

 

 

   
opens up or down

 

 

   

Guiding Questions

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Problem 2

Graph each quadratic function. For each function, identify the vertex, the root(s), the $${y-}$$intercept, and the axis of symmetry.

a.  $${f(x)=(x-5)(x-1)}$$

b.  $${g(x)={1\over2}x^2+5x+6}$$

c.  $${h(x)=-(x-3)^2+4}$$

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


Two quadratic functions are given below.

$${j(x)=(x-4)(x+2)}$$

$${k(x)=-(x-1)^2-9}$$

Sketch and compare the graphs of the two functions. How are they similar? How are they different?

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.

  • Include practice graphing quadratic functions from different forms of the equation.
  • Include review of previous lessons in the unit thus far.

Next

Describe transformations to quadratic functions. Write equations for transformed quadratic functions.

Lesson 9
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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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