Identify the Vertex
Vertex Form
Word Problems
Finite differences
Describe the Transformation
Axis of Symmetry
100

y=x2

(0, 0)

100

The height of a projectile is modelled by the equation y =-8(x - 2)2 +10 where f(x) is the height in metres and x is the seconds. After how many seconds is the projectile at its highest point? What is the highest point the projectile reaches?

What is 2 seconds and 10 metres.

100

Given the table of values, is the data linear, quadratic, or neither?

(x,  y)

(0,  1)

(1,  3)

(2,  9)

(3,  27)

(4,  81)

neither linear nor quadratic

100

y = x2 + 3

Opens up

no stretch/compression

up 3

vertex (0, 3)

100

y = 3(x - 4)2 - 6

x = 4

200

y = -2(x + 7)2

(-7, 0)

200

The height of a ball, h meters, in t seconds is given by the function h= -5(t - 3)2 + 46.5. That is the maximum height of the ball?

What is 46.5 meters

200

Given the table of values, is the data linear, quadratic, or neither?

(x,  y)

(-2,  -8)

(-1,  -1)

(0,  0)

(1,  1)

(2,  8)

quadratic

200

y = -(x + 4)2

opens down

left 4

vertex (-4, 0)

200

y = 3(x - 6)2 - 6

x = 6

300

y = 9(x + 5)2 - 10

(-5, -10)

300

The cost in C dollars of operating a machine per day is given by the function C= 2(x - 5)2 + 25. What is the minimum cost to operate the machine?

What is $25.

300

Given the table of values, is the data linear, quadratic, or neither?

(x,  y)

(0,  -3)

(1,  1)

(2,  5)

(3,  9)

(4,  13)


linear

300

y = -2x2 + 7

opens down

stretched by 2

up 7 

vertex (0, 7)

300

y = (x + 7)2 - 4

x = -7

400

y = -10x2 - 4

(0, -4)

400
Determine the euqation of a parabola, in vertex form, that passes through (11, 0) and has a vertex at (4, -35)

y = 5/7(x - 4)2 - 35

400

How can we tell by a table of values if the data is linear, quadratic, or neither?

If the first differences are constant = linear

If the second differences are constant = quadratic

If neither is constant = neither
400

y = (x - 3)2 +4

opens up

no vertical stretch or compression

right 3, up 4

vertex (3, 4)

400

y = (x +10)2 - 2

x = -10

500

y = -1000(x + 893)2 - 2009

(-893, -2009)

500

Find the equation of the parabola, in vertex form, that passes through (-4, 5) and has a vertex at (-2, -3)

y = 2(x + 2)2 - 3

500

Describe how you can tell if a function is quadratic, based on its equation, table of values, and graph

equation - highest exponent is 2

table of values - second differences are constant

graph - shape is a parabola

 
500

y = 1/2(x+2)2 +3

opens up

compressed by 1/2

 left 2, up 3

vertex (-2, 3)

500

y = (x + 0.5)2 - 2.5

x = -0.5

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