EngageNY
Deriving the Quadratic Formula
Where did that formula come from? Lead pupils on a journey through completing the square to discover the creation of the quadratic formula. Individuals use the quadratic formula to solve quadratic equations and compare the method to...
Illustrative Mathematics
Building a General Quadratic Function
Rewrite a quadratic function to easily see the transformations involved. The instructional task takes a general quadratic function and rewrites it into a form that shows the translations and scaling of the parent quadratic function. The...
Inside Mathematics
Quadratic (2009)
Functions require an input in order to get an output, which explains why the answer always has at least two parts. After only three multi-part questions, the teacher can analyze pupils' strengths and weaknesses when it comes to quadratic...
Mathematics Vision Project
Circles and Other Conics
Through a variety of hands-on activities and physical scenarios, this far-reaching unit leads learners through an exceptionally thorough exploration of circles and parabolas as conic sections. Geometric construction techniques are used...
Curated OER
The Quadratic Formula
Students solve quadratic function by completing the square. In this algebra lesson, students use the quadratic formula to factor quadratics and find the roots. They graph the parabola and identify its properties.
Curated OER
Quadratic Formula
Students explore the use of the quadratic formula. After solving problems using factoring and completing the square, students then use the quadratic formula. They evaluate the discriminate, determine the nature of the roots and...
Curated OER
Building a General Quadratic Function
Learners rewrite a general quadratic function by completing the square to see a new form of the function that more easily identifies the x-coordinate of the vertex and the two roots of the function.
EngageNY
Overcoming Obstacles in Factoring
What do you do when factoring doesn't work? Learners complete the square when faced with quadratic expression that don't factor traditionally. They then use factoring by grouping to solve polynomial equations.
Curated OER
Introduction into Quadratic Formula
Students explore various methods of solving quadratic equations. After practicing solving one problem with multiple methods, students compare and graph answers. They discuss which method of solving is best to use in a given situation.
Curated OER
Braking Distance
This real-life model of braking distance motivates learners to approach quadratic equations algebraically, numerically, graphically, and descriptively.
EngageNY
Mastering Factoring
Math class is full of drama—there are so many problems to work out! Pupils work out factoring problems. They use quadratic methods of factoring higher degree polynomials, in addition to factoring the sum and difference of two cubes.
Curated OER
Further Differentiation
In this further differentiation worksheet, students solve and complete 7 various types of problems. First, they sketch the graph of each equation using a stationary point. Then, students find the stationary points of each and describe...
EngageNY
Graphing Systems of Equations
Expand on learners' understanding of quadratic-linear systems. Building on the graphic understanding developed in the previous lesson, pupils learn algebraic methods of solving the systems.
Curated OER
Squaring Function of Natural Numbers
Eighth graders complete problems where they use the definition of exponents to expand the squaring function of natural numbers. In this squaring natural numbers lesson plan, 8th graders also identify squares form 0 - 12 and complete a...
Curated OER
Quadratic Functions And Their Graphs
Students engage in a classroom discussion about the shape of a parabola using real world examples. They define and discuss the important vocabulary and the teacher scaffolds by making clarification as necessary. For practice students...
EngageNY
Modeling with Polynomials—An Introduction (part 2)
Linear, quadratic, and now cubic functions can model real-life patterns. High schoolers create cubic regression equations to model different scenarios. They then use the regression equations to make predictions.
Illustrative Mathematics
Transforming the graph of a function
This activity guides learners through an exploration of common transformations of the graph of a function. Given the graph of a function f(x), learners generate the graphs of f(x + c), f(x) + c, and cf(x) for specific values of c. The...
EngageNY
Polynomial, Rational, and Radical Relationships
This assessment pair goes way beyond simple graphing, factoring and solving polynomial equations, really forcing learners to investigate the math ideas behind the calculations. Short and to-the-point questions build on one another,...
Alabama Learning Exchange
Classifying Complex Numbers
Imaginary numbers are a real thing. Scholars learn about complex numbers, real numbers, and imaginary numbers. They classify given numbers as strictly complex, strictly real, or strictly imaginary in an individual or group activity.