In a previous chapter, I tackled how to solve quadratics for two values of x by using factoring, completing the square, or the quadratic formula. In this chapter we'll take quadratic functions up a notch by using them -- and the parabolas they represent -- as "gateway" polynomials which teach us about the roots, zeros, intercepts, and graphing techniques that we'll use in higher-exponent polynomials later.
Parabolas -- Vertex Form Graphing & Vocab
In this video we get at the basics of graphing quadratic functions (parabolas) that are already in vertex form: axis of symmetry, domain, range, orientation, maximum/minimum, and intervals of increasing/decreasing. (For more on finding x-intercepts/zeros of quadratics, check out my solving quadratics chapter.)
How to put quadratics in "vertex form"
In this video I cover how to find all the same parabola stuff as last video -- vertex, axis of symmetry -- but for harder problems when the equation isn't already in vertex form, either by completing the square or using the "-b/2a trick". (For more on completing the square, check out my solving quadratics chapter.)
The Discriminant of a Parabola
This is a simple topic that teachers nonetheless find a way to make confusing (based on the number of questions I get about it). In this video I'll show you what the discriminant is, how to find it, and how to get this question right on the test.
Maximum & Minimum Word Problems
Sometimes teachers give you word problems based on parabolas, where they're asking you to maximize area of a picture frame or cattle pen, or minimize the product of a pair of numbers. These are their stories.