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FloridaMaths

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 the standard, vertex, and factored forms of a quadratic each reveal different key features, and how do you convert between them?

Recognize and use the standard, vertex, and factored forms of a quadratic function, identifying which key features each form reveals and converting between them (MA.912.AR.3.8, MA.912.AR.1.2).
A B.E.S.T. Algebra 1 EOC answer on the three forms of a quadratic, standard, vertex, and factored, what each reveals (y-intercept, vertex, zeros), and converting between them by expanding and completing the square.
11 min answer →

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

Graph a quadratic function and identify and interpret its key features: vertex, axis of symmetry, x- and y-intercepts, direction of opening, and maximum or minimum value (MA.912.AR.3.7, MA.912.F.1.3).
A B.E.S.T. Algebra 1 EOC answer on graphing parabolas (MA.912.AR.3), finding the vertex with x = -b/2a, the axis of symmetry, intercepts, direction of opening, and the maximum or minimum value.
11 min answer →

How do you model and solve real-world problems with quadratics, deciding when to use the vertex versus the zeros and which solutions to reject?

Model real-world situations with quadratic functions and solve, interpreting the vertex as a maximum or minimum and the zeros as start or end points, and rejecting solutions that do not fit the context (MA.912.AR.3.6, MA.912.AR.3.9).
A B.E.S.T. Algebra 1 EOC answer on quadratic applications (MA.912.AR.3), projectile motion and area models, using the vertex for the maximum or minimum and the zeros for landing or break-even, and rejecting impossible solutions.
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 using the quadratic formula from the reference sheet, and use the discriminant to determine the number and nature of the real solutions (MA.912.AR.3.4, MA.912.AR.3.5).
A B.E.S.T. Algebra 1 EOC answer on the quadratic formula from the reference sheet (MA.912.AR.3), substituting correctly, simplest radical form, and using the discriminant to count the real solutions.
11 min answer →

How do you solve a quadratic equation by factoring and applying 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 (MA.912.AR.3.4).
A B.E.S.T. Algebra 1 EOC answer on solving quadratics by factoring (MA.912.AR.3), setting the equation to zero, the zero-product property, and reading solutions as the x-intercepts of the parabola.
10 min answer →

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

Solve quadratic equations by taking square roots and by completing the square, including writing the equation in vertex form (MA.912.AR.3.4, MA.912.AR.3.8).
A B.E.S.T. Algebra 1 EOC answer on the square-root property and completing the square (MA.912.AR.3), when each applies, the plus-or-minus, simplest radical form, and producing vertex form.
11 min answer →