Students investigate and understand the features that are unique to quadratic functions, and they learn to factor quadratic equations in order to reveal the roots of the equation.
In Unit 7, Introduction to Quadratic Functions and Solutions, students take a closer look at quadratic functions. Because there is so much to cover on quadratic functions and equations, these concepts have been split over two units: Unit 7 and the last unit of the year, Unit 8. In Unit 7, students investigate and understand the features that are unique to quadratic functions, and they write quadratic equations into the equivalent intercept form in order to reveal the solutions of the equation. In Unit 8, students will learn about the vertex form and how to complete the square, along with digging into several real-world problems that involve quadratics.
In Topic A, students analyze features of quadratic functions as they are seen in graphs, equations, and tables. They draw on their understandings of linear and exponential functions to compare how quadratic functions may be similar or different.
In Topic B, students learn how to factor a quadratic equation in order to reveal the roots or solutions to the equation. They rewrite quadratic trinomials as the product of two linear binomials, and then using the zero product property, they determine the solutions when the function is equal to zero. Students also identify and compare solutions to quadratic functions that are represented as equations, tables, and graphs. Lastly, by determining the coordinates of the vertex of the parabola, students are able to sketch a reliable graph of the parabola using the $${x-}$$intercepts and the vertex as three defining points.
In Topic C, students bring together the concepts and skills from the unit in order to interpret solutions to quadratic equations in context. They look at examples involving projectile motion, profit and cost analysis, and geometric applications. Students will spend more time with these applications in Unit 8.
Pacing: 15 instructional days (13 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 7 and should be given on the suggested assessment day or after completing the unit.
?
Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
?
?
Quadratic functions | Greatest common factor |
Second difference | Zero Product Property |
Maximum/minimum | Intercept form |
Line of symmetry | Linear binomial |
Roots/solutions/$$x$$-intercepts | Quadratic trinomial |
Parabola | Difference of two squares |
Vertex | Perfect square trinomial |
?
F.IF.B.4
F.LE.A.2
Compare quadratic, exponential, and linear functions represented as graphs, tables, and equations.
F.IF.B.4
F.IF.C.7.A
Identify key features of a quadratic function represented graphically. Graph a quadratic function from a table of values.
F.IF.B.4
F.IF.B.6
F.LE.A.3
Calculate and compare the average rate of change for linear, exponential, and quadratic functions.
A.SSE.A.2
A.SSE.B.3.A
A.APR.A.1
Factor quadratic expressions using the greatest common factor. Demonstrate equivalence between expressions by multiplying polynomials.
F.IF.C.8.A
A.APR.B.3
Identify solutions to quadratic equations using the zero product property (equations written in intercept form).
A.SSE.A.1.A
A.SSE.B.3.A
Factor quadratic equations and identify solutions (when leading coefficient is equal to 1).
A.SSE.A.1.A
A.SSE.B.3.A
Factor quadratic equations and identify solutions (when leading coefficient does not equal 1).
A.SSE.A.1.A
A.SSE.A.2
A.SSE.B.3.A
Factor special cases of quadratic equations—difference of two squares.
A.SSE.A.2
A.SSE.B.3.A
Factor special cases of quadratic equations—perfect square trinomials.
A.SSE.B.3.A
F.IF.C.8.A
F.IF.C.9
Solve quadratic equations by factoring. Compare solutions in different representations (graph, equation, and table).
A.REI.B.4.B
Solve quadratic equations by taking square roots.
F.IF.C.7.A
F.IF.C.8.A
A.APR.B.3
Graph quadratic functions using $${x-}$$intercepts and vertex.
Key: Major Cluster Supporting Cluster Additional Cluster
?
?
?