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TexasMaths

Quadratic Functions and 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 determine the domain and range of a quadratic function, and connect its representations to the situation it models?

Determine the domain and range of quadratic functions and represent them using inequalities, and describe representations of quadratic functions in relation to their solutions and the real-world situations they model (TEKS A.6A, A.6B).
A STAAR Algebra I answer on the domain and range of quadratic functions (TEKS A.6A, A.6B), why the range is bounded by the vertex, representing with inequalities, and connecting representations to real-world models.
10 min answer →

How do you graph a quadratic function and identify its key attributes: vertex, axis of symmetry, intercepts, zeros, and maximum or minimum?

Graph quadratic functions on the coordinate plane and identify key attributes, including x-intercept, y-intercept, zeros, maximum or minimum value, vertex, and the axis of symmetry (TEKS A.7A, A.3B).
A STAAR Algebra I answer on graphing quadratic functions and reading key attributes (TEKS A.7A, A.3B) - vertex, axis of symmetry, intercepts, zeros, and maximum or minimum - from standard and vertex form, including hot-spot graphing.
11 min answer →

How do the parameters a, h, and k transform the parent function f(x) = x squared, and how do you write the transformed function?

Describe the effect on the graph of the parent function $f(x) = x^2$ when $a$ , $h$ , and $k$ change in $f(x) = a(x - h)^2 + k$ , and transform quadratic functions graphically and algebraically (TEKS A.7B, A.7C).
A STAAR Algebra I answer on transforming the parent function x squared (TEKS A.7B, A.7C) - vertical and horizontal shifts, reflections, and stretches or compressions - using the parameters a, h, and k in vertex form.
10 min answer →

How do you write a quadratic function from its real solutions, its graph, or a data set using vertex or standard form?

Write quadratic functions when given real solutions and graphs of their related equations, and write quadratic functions that fit data sets using vertex form or standard form (TEKS A.6C, A.8B).
A STAAR Algebra I answer on writing quadratic functions from real solutions (factored form), from a graph (vertex form), and from data (TEKS A.6C, A.8B), connecting zeros to factors.
10 min answer →