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OhioMaths

Quadratics

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 read its key features, the vertex, axis of symmetry, intercepts, and direction of opening?

Graph quadratic functions and identify the vertex, axis of symmetry, intercepts, and direction of opening from standard, factored, and vertex forms (Ohio F-IF.7a, F-IF.8a).
An Ohio Algebra I answer on graphing parabolas (F-IF.7a): the axis of symmetry x equals negative b over 2a, finding the vertex, reading intercepts from factored form, and how the three forms reveal different features.
12 min answer →

How do you use a quadratic model to answer real questions, like the maximum height of a projectile or when it lands, and how do you interpret the vertex and zeros?

Model and solve real-world problems with quadratic functions, interpreting the vertex as a maximum or minimum and the zeros as when a quantity is zero (Ohio A-CED.1, F-IF.4, A-REI.4b).
An Ohio Algebra I answer on quadratic applications (A-CED.1, F-IF.4): projectile and area models, reading the vertex as a maximum height or optimum, finding when a quantity is zero from the zeros, and interpreting in context.
12 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 any quadratic equation with the quadratic formula, and use the discriminant to determine the number and nature of the real solutions (Ohio A-REI.4b).
An Ohio Algebra I answer on the quadratic formula (A-REI.4b): substituting a, b, c correctly, simplifying the result, and reading the discriminant b squared minus 4ac to count the real solutions.
12 min answer →

How do you solve a quadratic equation by factoring, and why does setting each factor to zero give the solutions?

Solve quadratic equations by factoring and applying the zero-product property, after writing the equation in standard form equal to zero (Ohio A-REI.4b, A-SSE.3a).
An Ohio Algebra I answer on solving quadratics by factoring (A-REI.4b): writing the equation equal to zero, factoring, applying the zero-product property, and reading the solutions as the zeros of the parabola.
12 min answer →

How do you solve a quadratic by taking square roots, and how does completing the square turn any quadratic into vertex form you can solve?

Solve quadratic equations by taking square roots and by completing the square, and use completing the square to rewrite a quadratic in vertex form (Ohio A-REI.4a, A-REI.4b, F-IF.8).
An Ohio Algebra I answer on the square-root method and completing the square (A-REI.4a): solving x squared equals k with the plus-or-minus sign, completing the square step by step, and producing vertex form.
12 min answer →