By Factoring

Quadratic Formula

Word Problems

Graphing

Surprise!

Solve by factoring:
(x-2)(x+4)=0

x=2
x=-4

Solve using quadratic formula:
x^2-1=0

x=1
x=-1

If the dimensions of a rectangle are w=x and l=x-5 and the area is 36cm, what is w and l?

The width of the rectangle is 9cm and the length is 4cm

x^2-4=0
Graph using a table of values.
Show the real roots

x=2
x=-2

Factor
3x^2-45=0

3(x^2-15)=0

Solve by factoring:
x(x-1/2)=0

x=0
x=1/2

Solve by using quadratic formula:
x^2+x-2=0

x=1
x=-2

The length of a rectangular pool is 5m longer than its width. The area of the pool is 50m^2.
What are the dimensions of the pool?

The width of the pool is 5m and the length of the pool is 10m

Sketch the three possible outcomes when solving a quadratic equation.

1. Two distinct real roots
2. One real root
3. No real roots

Solve.
5x^2=8x

x=0
x=8/5 (or 1.6)

Solve by factoring:
x^2-6x+8=0

x=4
x=2
(x-4)(x-2)=0

Solve by using quadratic formula:
x^2+6x+5=0

x=-1
x=-5

The area of the front cover of a daily journal is 273cm^2 and the length is 8cm greater than the width. What are the dimensions of the cover?

The width of the front cover of the journal is 13cm and the length of the front cover is 21cm

Sketch a graph of 2x^2+x+2, showing the real roots (or x-intercepts)
You may use any method you want

There are no real roots.
The graph does not intersect the x-axis

Solve.
Round answers to the nearest hundredths
0.1=-2.2x^2-2.4x

x=-1.05
x=-0.04

Solve by factoring:
y^2-3y-10=0

y=5
y=-2
(y-5)(y+2)=0

Solve by using quadratic formula:
x^2+5x+2=0

x=(-5+root(17))/2
x=(-5-root(17))/2

A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the lawn and the flower bed is 165m^2. What is the width of the flower bed?

The width of the flower bed is 3.5m

x^2+x-6=0
Sketch the graph, showing the real roots
You may use any method you want

x=2
x=-3

Solve.
(x^2-1)/5=7

x=6
x=-6

Solve by factoring:
2x^2+11x+5=0

x= -5
x= -1/2
(x+5)(2x+1)=0

-2.2x^2-2.4x=0.1
*round to the nearest hundreth

x=-1.05
x=-0.04

Adding 19 to the square of the number of provinces in South Africa gives the square of the number of provinces in Canada. How many provinces are there in South Africa?

There are 9 provinces in South Africa
*there are 10 provinces in Canada

2x^2-x-3=0
Sketch the graph, showing the real roots
You may use any method you want

x=1.5
x=-1

Solve. Round to the nearest hundredth.
(2x^2)/2+(x)/3=1

x=0.85
x=-1.18