Intro to Quadratic Functions WS - Scottsdale Community College ...

Lesson 5a - Introduction to Quadratic Functions Practice Problems
Practice Problems
1. For each of the following Quadratics, (First one is done for you)
a) Identify the coefficients, a,b,c
b) Determine if the parabola opens up or down and state why.
c) Identify the y-intercept
d) Calculate the Vertex (Show your work)
e) Determine at least two points to the right and two points to the left of the vertex
f) Graph the function using the points you’ve identified and label the points
g) Draw a dashed line for the axis of symmetry
Identity the coefficients a, b, c a = 2, b = -4, c = -4
Which direction does the parabola
open? Why?
parabola opens up because a > 0
What is the y-intercept? (0, -4)
Calculate the Vertex First find the value of x
Now insert 1 into f(x) to find y
Vertex = (x, f(x)) = (1, –6)
Additional Points x f(x) = 2x 2 – 4x – 4 y (x,y)
-1 f(–1) = 2(–1) 2 – 4(–1) –
4
2 (–1, 2)
0 f(0) = 2(0) 2 – 4(0) – 4 –4 (0, –4)
1 f(1) = 2(1) 2 – 4(1) – 4 –6 (1, –6)
2 f(2) = 2(2) 2 – 4(2) – 4 –4 (2, –4)
3 f(3) = 2(3) 2 – 4(3) – 4 2 (3, 2)
15
(-2, 12)
10
Y
(4, 12)
-4
5
(-1, 2)
0
-2 0
-5
-10
(3, 2)
(0, -4) 2 (2, -4) 4
(1, -6)
X
6
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Lesson 5a - Introduction to Quadratic Functions Practice Problems
a)
b)
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Lesson 5a - Introduction to Quadratic Functions Practice Problems
c)
d)
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Lesson 5a - Introduction to Quadratic Functions Practice Problems
2. For each function, use your calculator to
a) Graph the function
b) Find the vertex (Calculate X and then use Calc/Value to find Y)
c) Find the x-intercepts of each function
d) Draw the graph and plot/label the points
a)
b)
c)
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Lesson 5a - Introduction to Quadratic Functions Practice Problems
d)
3. Solve each equation using your calculator. Draw the graph and plot/label the points
a)
b)
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Lesson 5a - Introduction to Quadratic Functions Practice Problems
c)
d)
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Lesson 5a - Introduction to Quadratic Functions Practice Problems
4. The function h(t) = -0.2t 2 + 1.3t + 15, y
where h(t) is height in feet, models the
height of an angry bird shot into the sky as a
function of time (seconds).
a) How high is the bird in the picture
above? Why?
b) After how many seconds does the bird reach
its highest point? Why?
c) How high is the angry bird at its highest point? Why?
d) After how many seconds does the angry bird hit the ground? Why?
e) If the bird is traveling at 15 feet per second, how far does the angry bird travel before it hits
the ground?
f) What is the practical domain of this function?
g) What is the practical range of this function?
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x

Lesson 5a - Introduction to Quadratic Functions Practice Problems
5. Suppose you set up a Hot Wheels Track and
decide to examine how the speed of the Hot
Wheels Car changes as it travels through the
loop. Look at the example to the left of how
the track might look. The example on the
right shows just the loop.
Draw a “Good” graph that shows how relationship between the speed of the car as it travels
through the loop might look. (Time versus Speed).
� Assume the time is in milliseconds and the speed is in mph.
� Start your graph when the car reaches the first dot.
� End your graph when the car reaches the second dot.
� What will the graph look like? Will it be a loop, open up, open down?
� Will it cross the x axis?
� What would the y-intercept represent?
� What would the vertex of the graph represent?
� Did you label your graph correctly?
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