y=x2
(0, 0)
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.
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
y = x2 + 3
Opens up
no stretch/compression
up 3
vertex (0, 3)
y = 3(x - 4)2 - 6
x = 4
y = -2(x + 7)2
(-7, 0)
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
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
y = -(x + 4)2
opens down
left 4
vertex (-4, 0)
y = 3(x - 6)2 - 6
x = 6
y = 9(x + 5)2 - 10
(-5, -10)
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.
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
y = -2x2 + 7
opens down
stretched by 2
up 7
vertex (0, 7)
y = (x + 7)2 - 4
x = -7
y = -10x2 - 4
(0, -4)
y = 5/7(x - 4)2 - 35
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 = neithery = (x - 3)2 +4
opens up
no vertical stretch or compression
right 3, up 4
vertex (3, 4)
y = (x +10)2 - 2
x = -10
y = -1000(x + 893)2 - 2009
(-893, -2009)
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
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 constantgraph - shape is a parabola
y = 1/2(x+2)2 +3
opens up
compressed by 1/2
left 2, up 3
vertex (-2, 3)
y = (x + 0.5)2 - 2.5
x = -0.5