A.6-A.8 Quadratic Functions and Equations

Determine the domain and range of quadratic functions and represent the domain and range using inequalities.

Write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x - h)2+ k), and rewrite the equation from vertex form to standard form (f(x) = ax2+ bx + c).

Write quadratic functions when given real solutions and graphs of their related equations.

Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry.

Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions.

Determine the effects on the graph of the parent function f(x) = x2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.

Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula.

Write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.