Nonlinear equations in one variable and systems of equations in two variables

Learning objectives

Solve quadratic equations by factoring, taking square roots, completing the square and using the quadratic formula

Use the discriminant to find the number of real solutions and to determine the constant that produces a required number of solutions

Solve absolute value, radical, rational and exponential equations, rejecting extraneous solutions

Relate the solutions of a quadratic equation to the factors of the expression and to the x-intercepts of its graph

Solve a system of one linear and one nonlinear equation and interpret the solutions as points of intersection

Determine how many points of intersection a line and a parabola have, and find the constant that makes them touch at exactly one point