Quadratic Functions Lesson 8 Solving Quadratic Equations using the ...

Quadratic Functions

Solving Quadratic Equations using the Quadratic Formula

Lesson 8

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Lesson Objectives ^Z

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Common Core State Standards:

Standards for Mathematical Practice:

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Lesson Resources:

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Lesson Breakdown:

Day 1

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Day 2

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Quadratic Functions

Lesson 8

Solving Quadratic Equations using the Quadratic Formula

Steps and Learning Activities

Day 1 Quadratic Formula Opener

Anticipated Student Responses and Teacher Support

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Students may need assistance setting up the quadratic equation. Remind them that they need to distribute the linear pairs to find the quadratic equation and set that equal to the new area.

Posing the Task hdEZZ ZZ ZZZZZ

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tZ Remind students what happens when the denominator of a fraction is equal to zero.

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,ZZ Have the student's research how the quadratic formula is derived or have the students derive it themselves. This concept will be addressed in depth during Algebra 2 or Integrated Mathematics III.

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Remind the students that they must be careful when substituting the coefficients into the equation that they MUST be in the correct place or their calculations and solutions will be incorrect. Often times, if b is negative, the student may forget to make the value positive due to the formula.

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Quadratic Functions

Lesson 8

Solving Quadratic Equations using the Quadratic Formula

Steps and Learning Activities

Day 2 Discovering the Discriminant Activity Z ,ZZZZZ ZZ ZZZZ ZZZ ZZZZZ ZZZ ZZZZ Posing the Task: hZZ &ZZZ ZZ Z

Day 3 Quadratic Formula Problem Set dY&Z ZZdZZ ZZZZ dZZ ZZ ZZZZ, ZZZZ ZZ ZZZZZZ dZZZ ZZZ ZZ Z

Anticipated Student Responses and Teacher Support

tZZZZ ZZZZZ "The definition is referring to a quadratic equation, not a function. The graphs represent the nature of a quadratic equation to connect that the real roots are shown by the function intercepting the x-axis. When the function does not intersect the x-axis, then the equation will have complex roots, or no real zeros."

Remind students to be careful when computing the discriminant that has negative values. This calculation may result in the wrong number of roots.

,ZZZZ Z Remind the students to rewrite the equations in standard form to determine the values of a, b and c. If not, this will cause a sign error and result in incorrect solutions. ,ZZZZZZ Z Remind students that they can use the discriminant to check to see how many roots there will be for the quadratic equation. They can also substitute the value of x into the equation and solve to see if it is correct. Some students may need to write out the values for a, b and c to help them determine the discriminant.

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Quadratic Functions

Lesson 8

Solving Quadratic Equations using the Quadratic Formula

Steps and Learning Activities

Day 4 Performance Task dZZ ZZZZZ Z ZZZZ dZZZ ZZ ZZ ZZZZ ZZ Z

Anticipated Student Responses and Teacher Support

,ZZ/ZZZZ "Refer to the diagram that shows how far the pitchers box is away from the beginning of the platform, the hole, and where the platform ends." dZZZZZ ZZ/ZZ "What would it mean if the solution were negative?" /Z "Well let's draw the parabola, what does it look like? What is its path?" /ZZZZ "So, is that the whole parabola?" EZ "Where would the rest of the parabola go?" /Z "Correct. So where is our negative solution?" /Z "Then, that means that the negative solution is extraneous in the context of this situation."

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Quadratic Functions

Solving Quadratic Equations using the Quadratic Formula

Lesson 8

Resources for English Learners

English Language Objective(s): x >ZZZZZ x tZZZZZ

EnglishLearners Unit Vocabulary: Every Day Terms/ Phrases (Tier 1) Z Z hZ ZZZ

General Academic Terms (Tier 2)

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EL Strategies: dZZZZZZ>Z,ZZZ Z>ZZZZZZZZZ ZWZZZZZZZZK> ZZZZZZZ&Z ZZZZ Z

Analysis of CCSS Implementation

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