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GeorgiaMaths

Quadratic Functions and Equations

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you solve a quadratic by taking square roots or by completing the square, and how does completing the square give vertex form?

Solve quadratic equations by the square-root property and by completing the square, and use completing the square to rewrite a quadratic in vertex form (A.PAR, Patterning and Algebraic Reasoning).
A Georgia Milestones Algebra: Concepts & Connections answer on solving quadratics by the square-root property and by completing the square, adding the square of half the linear coefficient to form a perfect-square trinomial, and using completing the square to convert standard form to vertex form.
11 min answer →

How do you graph a parabola, and how do you find its vertex, axis of symmetry, and intercepts?

Graph quadratic functions and identify key features: the vertex, the axis of symmetry, the y-intercept, the x-intercepts (zeros), and the direction of opening (A.FGR, Functional and Graphical Reasoning).
A Georgia Milestones Algebra: Concepts & Connections answer on graphing quadratic functions and their key features: the vertex from the axis of symmetry formula, the direction of opening from the sign of a, the y-intercept, the x-intercepts (zeros), and whether the vertex is a maximum or minimum.
10 min answer →

How do you use a quadratic model to answer real questions, and when do you use the vertex versus the zeros?

Build and use quadratic models for situations such as projectile motion and area, using the vertex for maximum or minimum values and the zeros for boundary values, and interpreting solutions in context (A.FGR and A.MM, Functional and Graphical Reasoning and Modeling).
A Georgia Milestones Algebra: Concepts & Connections answer on modeling with quadratic functions: projectile-motion and area models, using the vertex for maximum or minimum values and the zeros for ground level or break-even, rejecting unrealistic solutions, and stating answers with units.
11 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 with the quadratic formula, and use the discriminant to determine the number and type of real solutions (A.PAR, Patterning and Algebraic Reasoning).
A Georgia Milestones Algebra: Concepts & Connections answer on the quadratic formula and the discriminant: substituting a, b, and c correctly, simplifying to simplest radical form, and using the discriminant to count real solutions and connect them to the parabola's x-intercepts.
10 min answer →

How do you solve a quadratic equation by factoring, and why does setting it equal to zero first matter?

Solve quadratic equations by factoring using the zero-product property, after writing the equation in standard form (A.PAR, Patterning and Algebraic Reasoning).
A Georgia Milestones Algebra: Concepts & Connections answer on solving quadratic equations by factoring: writing the equation in standard form equal to zero, factoring, applying the zero-product property, and connecting the solutions to the x-intercepts of the parabola.
10 min answer →

How does vertex form show the transformations of a parabola, and how do you read the vertex and direction directly from it?

Use vertex form to describe transformations of the parent function and to read the vertex, direction, and stretch of a quadratic (A.FGR, Functional and Graphical Reasoning).
A Georgia Milestones Algebra: Concepts & Connections answer on transformations of quadratic functions using vertex form, reading horizontal and vertical shifts, reflections, and vertical stretches or compressions from a in vertex form, and identifying the vertex directly.
10 min answer →