Curriculum / Math / 9th Grade / Unit 8: Quadratic Equations and Applications / Lesson 6
Math
Unit 8
9th Grade
Lesson 6 of 15
Jump To
Derive the quadratic formula. Use the quadratic formula to find the roots of a quadratic function.
The core standards covered in this lesson
A.REI.B.4.A — Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)² = q that has the same solutions. Derive the quadratic formula from this form.
The foundational standards covered in this lesson
A.CED.A.4 — Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Fully deriving the quadratic formula requires that students know how to add fractions with unlike denominators involving a variable. This does not fully come up until Algebra 2, so students will likely need to be guided through this part of the derivation. See the Notes for Anchor Problem #2 for sample solution steps.
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Solve the equation by completing the square. Show each step clearly.
$${3x^2-5x+1=0}$$
A quadratic equation is written below in standard, general form.
$${ax^2+bx+c=0}$$
Solve for $$x$$ by completing the square as you did in Anchor Problem #1.
Recall the equation from Anchor Problem #1: $${3x^2-5x+1=0}$$.
Use the quadratic formula to determine the exact roots of the equation.
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Use the quadratic formula to find the exact roots of the equation below.
$${-4x^2-3x+8=y}$$
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.
Lesson 5
Lesson 7
Topic A: Deriving the Quadratic Formula
Describe features of the vertex form of a quadratic function and write quadratic equations in vertex form from graphs.
A.SSE.B.3 F.IF.B.4 F.IF.C.8
Complete the square.
A.SSE.B.3.B
Complete the square to identify the vertex and solve for the roots of a quadratic function.
A.REI.B.4.B A.SSE.B.3.B
Solve and interpret quadratic applications using the vertex form of the equation.
A.SSE.B.3.B F.IF.C.8.A
Convert and compare quadratic functions in standard form, vertex form, and intercept form.
F.IF.B.4 F.IF.C.9
A.REI.B.4.A
Determine the number of real roots of a quadratic function using the discriminant of the quadratic formula.
A.REI.B.4.B F.IF.C.7.A
Graph quadratic functions from all three forms of a quadratic equation.
F.IF.C.7.A
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
Topic B: Transformations and Applications
Describe transformations to quadratic functions. Write equations for transformed quadratic functions.
F.BF.B.3
Graph and describe transformations to quadratic functions in mathematical and real-world situations.
Write and analyze quadratic functions for projectile motion and falling bodies applications.
A.CED.A.2 F.IF.C.8.A F.IF.C.9
Write and analyze quadratic functions for geometric area applications.
A.CED.A.2 F.IF.C.8.A
Write and analyze quadratic functions for revenue applications.
A.CED.A.2 F.BF.A.1.B F.IF.C.8.A
Solve and identify solutions to systems of quadratic and linear equations when two solutions are present.
A.REI.C.7 A.REI.D.11
Solve and identify solutions to systems of quadratic and linear equations when two, one, or no solutions are present.
See all of the features of Fishtank in action and begin the conversation about adoption.
Learn more about Fishtank Learning School Adoption.
Yes
No
Access rigorous, relevant, and adaptable math lesson plans for free