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TennesseeMaths

Quadratic Equations

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you graph a quadratic function and identify its vertex, axis of symmetry, intercepts, and direction of opening?

Graph quadratic functions and show key features including the vertex, axis of symmetry, intercepts, maximum or minimum, and direction of opening (TN A1.F.IF.D.7a).
A TNReady Algebra I answer on graphing quadratics (TN A1.F.IF.D.7a), finding the vertex with the axis of symmetry, the y-intercept and x-intercepts, the direction of opening, and reading maximum or minimum.
11 min answer →

How do you use a quadratic model to answer real-world questions about maximum height, landing time, or area?

Model real-world situations with quadratic equations and interpret the solutions, including projectile motion and area problems (TN A1.A.REI.B.4, A1.A.CED.A.1).
A TNReady Algebra I answer on quadratic applications (TN A1.A.REI.B.4, A1.A.CED.A.1), projectile motion, the vertex as a maximum, the zeros as start and end, area problems, and rejecting nonviable roots.
11 min answer →

How do you use the quadratic formula to solve any quadratic, and what does the discriminant tell you about the number of real solutions?

Solve quadratic equations by applying the quadratic formula, and use the discriminant to determine the number of real solutions (TN A1.A.REI.B.4).
A TNReady Algebra I answer on the quadratic formula from the reference sheet (TN A1.A.REI.B.4), substituting correctly, simplest radical form, and using the discriminant to count real solutions.
11 min answer →

How do you solve a quadratic equation by factoring, and why must one side be zero first?

Solve quadratic equations in one variable by factoring, using the zero-product property after writing the equation equal to zero (TN A1.A.REI.B.4).
A TNReady Algebra I answer on solving quadratics by factoring (TN A1.A.REI.B.4), setting the equation to zero, factoring, and applying the zero-product property to find both solutions.
10 min answer →

How do you solve a quadratic by taking square roots or by completing the square, and when is each the right method?

Solve quadratic equations by taking square roots and by completing the square, recognizing when each method applies (TN A1.A.REI.B.4).
A TNReady Algebra I answer on solving quadratics by the square-root property and by completing the square (TN A1.A.REI.B.4), including the plus-or-minus step and converting to vertex form.
11 min answer →