PRECALculus 11 Quadratics
Specific Curriculum Outcomes
RF03 Students will be expected to analyze quadratic functions of the form $y=a(x  p)^2 + q$ and determine the vertex, domain and range, direction of opening, axis of symmetry, xintercept, and yintercept.
RF04 Students will be expected to analyze quadratic functions of the form $y=ax^2 + bx + c$ to identify characteristics of the corresponding graph, including vertex, domain and range, direction of opening, axis of symmetry, xintercept and yintercept, and to solve problems.
RF05 Students will be expected to solve problems that involve quadratic equations.
RF01 Students will be expected to factor polynomial expressions of the following forms where a, b, and c are rational numbers: $ax^2 + bx + c$ , $a^2x^2  b^2y^2$ , $a[f(x)]^2 +b[f(x)] +c$ , $a^2[f(x)]^2  b^2[g(y)]^2$
RF03 Students will be expected to analyze quadratic functions of the form $y=a(x  p)^2 + q$ and determine the vertex, domain and range, direction of opening, axis of symmetry, xintercept, and yintercept.
RF04 Students will be expected to analyze quadratic functions of the form $y=ax^2 + bx + c$ to identify characteristics of the corresponding graph, including vertex, domain and range, direction of opening, axis of symmetry, xintercept and yintercept, and to solve problems.
RF05 Students will be expected to solve problems that involve quadratic equations.
RF01 Students will be expected to factor polynomial expressions of the following forms where a, b, and c are rational numbers: $ax^2 + bx + c$ , $a^2x^2  b^2y^2$ , $a[f(x)]^2 +b[f(x)] +c$ , $a^2[f(x)]^2  b^2[g(y)]^2$
Activities
 Desmos Polygraph: Parabolas  This is a great online activity for a class to try out.One student selects a parabola. Another student tries to guess which parabola was chosen by asking yes/no questions. Student practice mathematical communication in this activity.
 Will It Hit the Hoop, a Desmos activity from Dylan Kane  The first set of graphs involves dragging two points on the quadratics to fit the curve of the shot. The second set of graphs puts the equations in vertex form, and has the students adjust sliders to change the coefficients.
 M&M Catapult Project from Sweeney Math  Students use experimental data from firing M&M's from a small catapult on the floor to calculate the equation of a quadratic. They then place the catapult on a desk and have to use the equation to predict where the M&M will land.
 Match My Parabola activity from Michael Fenton  Develop your students’ graphing abilities with this series of quadratic function challenges. Use Desmos to explore these questions for added interaction. I created an extension to this problem on Desmos... "The Danger Zone"
 Factoring Quadratics from Open Middle  Fill in the empty boxes (a, b and c in ax^2 +bx +c=0) with whole numbers 0 through 9, using each number at most once, so that the solutions are integers. How many different possibilities are there? How many give you 2 integer solutions, how many give you 1 integer solution, how many give you noninteger solutions (like rationals), and how many give you no solutions?
 Two Squares are Equal from Illustrative Mathematics  This classroom task is meant to elicit a variety of different methods of solving a quadratic equation. Some are straightforward; some are simple but clever; some use tools (using a graphing calculator). Some solution methods will work on an arbitrary quadratic equation, while others may have difficulty or fail if the quadratic equation is not given in a particular form, or if the solutions are not rational numbers.
 Completing the Literal Square from Bob Lochel  Using the "box" method for teaching multiplication of binomials can be extended to completing the square and may reach more visual learners.
 Applications of Quadratic Functions from Bob Lochel  A project for students to investigation an application of parabolas.
 Forming Quadratics Lesson from the Mathematics Assessment Project  This lesson unit is intended to help you assess how well students are able to understand what the different algebraic forms of a quadratic function reveal about the properties of its graphical representation. In particular, the lesson will help you identify and help students who have the following difficulties: Understanding how the factored form of the function can identify a graph’s roots; Understanding how the completed square form of the function can identify a graph’s maximum or minimum point; Understanding how the standard form of the function can identify a graph’s intercept.


 Factoring Trinomials Puzzle from Dan Wekselgreene  A puzzle for students to put together... more fun than just doing a worksheet. This puzzle, once assembled, instructs students to tell you a joke.