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Quadratic Equations

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you solve a quadratic equation by completing the square, and how does it produce vertex form?

Solve quadratic equations by completing the square, and use completing the square to rewrite a quadratic in vertex form (A.EI.6).
A Virginia SOL Algebra I answer on completing the square: the half-the-b, square-it step, solving by completing the square, and rewriting a quadratic into vertex form.
8 min answer →

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

Solve quadratic equations using the quadratic formula, and use the discriminant to determine the number and nature of the real solutions (A.EI.6).
A Virginia SOL Algebra I answer on the quadratic formula and the discriminant: identifying a, b, c, substituting into the formula, simplifying radical solutions, and reading the discriminant for the number of real roots.
9 min answer →

How do you solve a quadratic equation by factoring, using the zero product property?

Solve quadratic equations in one variable by factoring and applying the zero product property, and interpret the solutions as the zeros of the related function (A.EI.6).
A Virginia SOL Algebra I answer on A.EI.6: setting a quadratic equal to zero, factoring, applying the zero product property, and connecting the solutions to the x-intercepts of the parabola.
9 min answer →

How do you solve a quadratic equation by taking square roots, and when is that method the right choice?

Solve quadratic equations of the form x^2 = k or a(x - h)^2 = k by taking square roots, including the plus-or-minus sign, and recognize when there is no real solution (A.EI.6).
A Virginia SOL Algebra I answer on solving quadratics by taking square roots: isolating the squared term, the plus-or-minus sign, simplifying radical solutions, and recognizing no-real-solution cases.
8 min answer →