Unit 5: Quadratic Functions & Equations (Math 20-1)
Zeros/roots/intercepts; vertex form; completing the square; quadratic formula & discriminant; applications.
Standard \(ax^2+bx+c\)
Vertex \(a(x-h)^2+k\)
Axis \(x=-\\frac{b}{2a}\)
Discriminant \(\\Delta=b^2-4ac\)
Applications & Modelling
What You Should Be Able To Do
- Identify and interpret zeros/roots/x-intercepts and the y-intercept.
- Write vertex form \(a(x-h)^2+k\) by completing the square; state vertex & axis.
- Use the quadratic formula and discriminant to classify and find roots.
- Graph parabolas and solve contextual problems (max/min, intercepts, given \(y\)).
Progress autosaves to this device.
Video Library
Zeros & Intercepts
Identify x- and y-intercepts and what they mean.
youtube.com – “quadratic zeros intercepts examples”Completing the Square
Convert \(ax^2+bx+c\) to \(a(x-h)^2+k\).
youtube.com – “completing the square vertex form”Quadratic Formula & Discriminant
Classify roots with \(\\Delta\); compute exact/decimal roots.
youtube.com – “quadratic formula and discriminant”Applications & Modelling
Max/min, projectile motion, revenue/area models.
youtube.com – “quadratic applications max min word problems”Interactive Tools
Form Converter & Completing the Square
Quadratic Formula & Discriminant
| Quantity | Value |
|---|
Graph the Parabola
Enter \(y=ax^2+bx+c\). Window defaults to \([-10,10]\) for both axes.
Applications Calculator
Model \(y=ax^2+bx+c\). For projectiles in metres/seconds, \(a\) is typically negative.
Unit 5 Quizzes
Downloadable Review
Quick Practice Scratchpad
Try: convert \(y=2x^2-8x+1\) to vertex form; classify roots for \(y=x^2+4x+8\); solve \(y=-5t^2+30t+2\) for ground hits.