Help

- Watch and Read
- - Let's Start Thinking
  - Finding the Vertex From Vertex Form
  - Finding an Equation Given the Vertex
  - Converting a Factored Form Equation to a Vertex Form Equation
  - Try This Revisited
  - Wrap-Up
  - Alternative Format
- Review
- - Explore This 1
  - Check Your Understanding 1
  - Check Your Understanding 2
  - Check Your Understanding 3
- Practise
- - Exercises
  - Answers
  - Solutions

Let's Start Thinking

Exploring Vertex Form

Three Forms of Quadratic Relations

	Example	General Form	Observations
Standard Form	\(y=2x^2+12x+10\)	\(y=\class{timed add2-hl2 remove3-hl2}{a}x^2+bx+\class{timed add3-hl2 remove4-hl2}{c}\)	direction of opening: \(a \gt 0 \implies \) opens up \(a \lt 0 \implies \)opens down \(y\)-intercept is \(c\)
Factored Form	\(y=2(x+1)(x+5)\)	\(y=\class{timed add11-hl2 remove6-hl2}{a}(x-\class{timed add6-hl2 remove7-hl2}{r})(x-\class{timed add6-hl2 remove7-hl2}{s})\) (Works best when the zeros are integers)	\(a\) indicates the direction of opening zeros are \(r\) and \(s\) from the zeros, we can find the axis of symmetry and vertex
Vertex Form	\(y=2(x+3)^2+8\)	\(y=a(x-h)^2+k\)	vertex is ???

Example

General Form

Observations

\(a\) indicates the direction of opening
zeros are \(r\) and \(s\)
from the zeros, we can find the axis of symmetry and vertex

vertex is ???

Paused Finished

Slide /

Learning Goals

Determine the vertex of a quadratic relation given the vertex form equation.
Determine the vertex form equation of a quadratic relation given the vertex.
Convert the factored form equation of a quadratic relation to the vertex form equation.

Try This

Recall

Profit is the amount gained or lost after subtracting all costs from the money collected.

A live theatre company has analyzed the profit it makes, \(P\) (in thousands of dollars), based on different ticket prices, \(x\) (in dollars). They have found that their profit is modelled by \(P=-\dfrac{1}{135}(x-45)^2+10\).

Why does a parabola opening down model this situation?
What ticket price will produce the maximum profit?

Let's Start Thinking

Slide Notes

Glossary

All Slides

Navigation

Exploring Vertex Form

Three Forms of Quadratic Relations

Learning Goals

Try This