Quadratics
Worksheet 6
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1. Consider the quadratic function: y = 2x2 - 4x - 6
(
a) Graphing form
)
Y = 2x2 – 4x – 6
Y = 2(x2 – 2x) – 6
Y = 2(x2 – 2x + 1 - 1) - 6
Y = 2(x2 – 2 x+ 1) – 2 – 6
Y = 2(x – 1)2 – 8
b) Factored form
(
)(
)
Y = 2x2 – 4x – 6
Y = 2x2 – 6x +2x – 6
Y = 2x(x - 3) + 2(x – 3)
Y = (x – 3)(2x + 2)
c) Standard form
Y = 2x2 – 4x – 6
d) Graph the function on graph paper.
e) Find the X intercept(s).
Y = (x – 3)(2x + 2)
X – 3 = 0 AND 2x + 2 = 0
The X intercepts are (3 , 0) and (-1 , 0) or “3” and “-1”
f) Find the Y intercept.
Y = 2x2 – 4x – 6
Y = 2(0)2 – 4(0) – 6
The Y intercept is (0 , -6) or “-6”
2. Consider the quadratic function: y = - 0.5x2 - 3x + 3.5
(
a) Graphing form
)
Y = - 0.5x2 – 3x + 3.5
Y = - 0.5[x2 + 6x] + 3.5
Y = - 0.5[x2 + 6x + 9 - 9] + 3.5
Y = - 0.5[x2 + 6x + 9 ] + 4.5 + 3.5
Y = - 0.5(x + 3)2 + 8
b) Factored form
Y = -0.5[x2 + 7x - x - 7]
Y = -0.5[x(x + 7) -1(x + 7)]
Y =-0.5 (x – 1)(x + 7)
y = - 0.5x2 - 3x + 3.5
d) Graph the function on graph paper.
e) Find the X intercept(s).
Y =0.5 (x – 1)(x + 7)
X intercepts at (1 , 0) and (-7 , 0)
y = - 0.5(0)2 – 3(0) + 3.5
Y intercept at (3.5 , 0)
)(
Y = - 0.5x2 – 3x + 3.5
Y = -0.5[x2 + 6x - 7]
c) Standard form
f) Find the Y intercept.
(
)
3. A projectile moves according the equation ( )
H = vertical distance (height), x = horizontal distance (range)
a)
b)
c)
d)
e)
(
)
Write the function in graphing form
Make a “rough” graph the function (not on graph paper).
What is the maximum height of the projectile?
How far does it go (range) before the projectile reaches the maximum height?
How long is the projectile in the air? (find the x intercepts)
4. A projectile moves according the equation
H = height, t = time in seconds
a)
b)
c)
d)
e)
( )
.
(
)
Write the function in graphing form
Make a “rough” graph the function (not on graph paper).
What is the maximum height of the projectile?
How many seconds pass before the projectile reaches the maximum height?
For how many seconds is the projectile in the air?
5. A rectangular garden is 50 feet wide and 40 feet long. A sidewalk is created around the outside
that has a total area of 500ft2. How wide is the sidewalk?