How to solve a complicated looking quadratic equation by substitution.
How to graph parabolas that are wide or skinny or upside down without making a table of values.
How to graph a quadratic inequality.
How to label the roots of a quadratic polynomial, solutions to a quadratic equation, and x-intercepts or roots of a quadratic function.
How to solve quadratic equations by factoring.
How to solve a quadratic inequality using a sign chart.
How to derive the quadratic formula by completing the square.
How to use the shape of a parabola to find a maximum or minimum.
How to know which method to use when solving a quadratic equation.
How to use the discriminant to know the number and type of solutions to a quadratic.
How to solve quadratic equations using square roots.
How to find the vertex, intercepts, domain and range of a quadratic graph.
How to complete the square.
How to understand basic transformations of a polynomial graph.
How to evaluate a polynomial in function notation.