Solve Quadratic Equations

Unit 12

Common Core Says...

 

Big Picture Lesson Planning for the Common Core

Week #30 Factoring

• Factor quadratic equations (A.SSE.3a)
• Solve quadratic equations by factoring (A.SSE.3a)

Week #31 Completing the square

• Complete the square (A.SSE.3b)
• Use completing the square to find maximum and minumum values (F.IF.8)
• Derive the quadratic formula using the form (x-p)^2 = q (A.REI.4)

Week #32 Quadratic formula and systems

• Use the quadratic formula to solve quadratic equations (A.REI.4)
• Be able to identify which process is best to solve a quadratic equation (A.REI.4)
• Solve a system of equations containing one quadratic and one linear function (A.REI.7)

Lesson Ideas

All of these resources and more can be found in the livebinder below.

Common Core Standards

A.SSE.3.a Factor a quadratic expression to reveal the zeros of the function it defines.

A.SSE.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.*

A.REI.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.

A.REI.4.b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b.

A.REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = 3x and the circle x2 + y2 = 3.

A.REI.11Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* (Emphasize linear, absolute value, and exponential functions)Video Explaination

F.IF.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.

N.RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

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