Algebra 1 – Module 7: Quadratic Functions Name...2020/03/27 · b. When trying to determine the y-intercept of a quadratic function, which form is easier to use: factored form or

Algebra 1 – Module 7: Quadratic Functions Name _______________________________ Q – 4.1: Quadratic Functions Written in Factored Form Per _____ Date _______________________

© 2016 Hawaii Department of Education Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license. 1

Part I: Warm-up 1. Solve for r: 4(3 – 2r) = r – 6(r + 5) 2. Determine the product of

3. Solve for g: 4. Graph , then use your

graph to solve the equation

Part II: Exploring quadratic functions written in factored form. 5. Complete the table values for . Then, use your table to graph .

0

1

2

3

4

5

6

x +11( ) x − 7( )

L = p+ 2gK

f (x) = −x2 +3

−x2 +3= 2

f (x) = x −1( ) x − 5( ) f (x)

x f (x)



6. Based on the shape of the graph of , what type of function is ? 7. Using either your graph or the table of values, state the x-intercepts of . 8. Analyze the coordinates of the x-intercepts of in relation to the symbolic representation of

.

a. Discuss with your partner what you notice and write down any ideas you discussed.

b. Based on what you discussed with your partner, what will be the x-intercepts of the following functions? • will have x-intercepts at _____________ and _____________

• will have x-intercepts at _____________ and _____________







9. In general, any quadratic function written in the form will have x-intercepts at

_____________ and _____________ . Consequently, the function will have x-

intercepts at _____________ and _____________ .

10. Refer back to your graph in question #5. State the coordinates of the vertex of .

f (x) = x −1( ) x − 5( ) f (x)

f (x) = x −1( ) x − 5( )

f (x)f (x)

g(x) = x − 4( ) x − 7( )

h(x) = x − 2( ) x − 9( )

m(x) = x + 4( ) x + 7( )

n(x) = x +1( ) x + 5( )

c(x) = x +3( ) x − 6( )

d(x) = x −31( ) x + 75( )

p(x) = x x −8( )

r(x) = x x + 25( )

q(x) = x − r( ) x − s( )

p(x) = x + r( ) x + s( )

f (x) = x −1( ) x − 5( )



11. Recall that in the previous module, you learned a quick strategy for graphing a quadratic function:

• First, determine the location of the vertex. • Then, the second point will be 1 unit to the right and 1 unit up from the vertex. • Then, the third point will be 2 units to the right and 4 units up from the vertex. • Then, reflect the points over the axis of symmetry. • Finally, sketch the parabola through those 5 points.

Analyze your graph of . Does your graph match these 5 steps? 12. In your graph of , compare the x-coordinate of the vertex to the x-coordinates

of the x-intercepts. Discuss with your partner what you notice and write down any ideas that you discussed.

13. For , you’ve already determined that the x-coordinate of the vertex is .

a. Determine the value of … show your work.

b. Using your answer in part a (above), compare the value of to the coordinates of the vertex of . What do you notice?

14. For each function below, show the location of the x-intercepts and then determine the coordinates

of the vertex. Finally, sketch the graph of the function. a. b.

x-intercepts: _____________________ x-intercepts: _____________________ vertex: _____________ vertex: _____________

f (x) = x −1( ) x − 5( )

f (x) = x −1( ) x − 5( )

f (x) = (x −1)(x − 5) x = 3

f (3)

f (3)f (x) = (x −1)(x − 5)

g(x) = x − 4( ) x − 2( ) h(x) = x −1( ) x +3( )



Part III: Summarize and practice.

15. Look back at your work and answers to questions 12 – 14. Discuss with your partner how you would explain to someone a process for determining the coordinates of the vertex of a quadratic function written in the form . Then, write down a few clear, simple steps to summarize what you discussed.

16. Use the steps you just summarized (in question #15 above) to determine the x-intercepts and the

vertex of each of the following functions. Show the work you did to determine the vertex. Then, make a quick sketch of the graph of the function (you do NOT have to draw the graph to scale).

a. b. c. d.

e. f.

q(x) = x − r( ) x − s( )

H (x) = x − 9( ) x − 5( ) j(x) = x +10( ) x − 2( )

k(x) = x x + 4( ) L(x) = − x +8( ) x + 2( )

m(x) = −x x −3( ) g(x) = 2 x + 5( ) x − 7( )

Algebra 1 – Module 7: Quadratic Functions Name _______________________________ Q – 4.2: Graphing Quadratic Functions in Factored Form Per _____ Date _______________________


Part I: Warm-up

1. Solve for p: 2. Determine the product of

Part II: Using the key features of a quadratic function to determine its graph 3. In the previous lesson you learned how to determine the x-intercepts and the vertex of a quadratic

function written in factored form: . State the steps that can be used to explain to someone how to determine the x-intercepts and vertex of .

4. Using the steps you stated above, draw the graph of

5. Determine the value of and plot the point on your graph above. 6. What is the name of the point on the graph that helps us find?

−12(4p−14)− p+ 5< 33 r − 9( ) r − 5( )

q(x) = x − r( ) x − s( )q(x)

P(x) = x + 2( ) x − 4( )

P(0)

P(0)



7. Without graphing, determine the y-intercept of each of the following functions. Show how you determined your answer.

a. b. c. d. 8. State the coordinates of the y-intercept of the graph of and briefly explain 2

ways to determine the y-intercept:

a. The coordinates of the y-intercept of : _____________________

b. Using the graph of , I can determine the y-intercept by _________________________

_________________________________________________________________________ .

c. Using the symbolic representation of , I can determine the y-intercept by

_________________________________________________________________________ .

9. Consider the function

a. Determine the y-intercept of . Show how you determined your answer. b. is given in factored form. Rewrite so it is expressed in STANDARD form of a

quadratic function. Show how you determined your answer. c. Using your answer for question b, determine the y-intercept by finding the value of

d. Compare your answer for question a to your answer for question c. What do you notice?

H (x) = x − 9( ) x − 5( ) j(x) = x +10( ) x − 2( )

k(x) = −3 x −1( ) x +3( ) L(x) = − x +8( ) x + 2( )

g(x) = −2 x + 5( ) x − 7( )

g(x)

g(x)

g(x)

h(x) = x + 5( ) x −1( )

h(x)

h(x) h(x)

h(0).



10. Rewrite each of the following functions in STANDARD form. Then, use the standard form to determine the y-intercept of the graph of the function.

a. b. c. 11. Discuss the following questions with a partner and summarize what you discussed:

a. For each function in question #10 above, compare the coordinates of the y-intercept to the standard form of the function. What do you notice?

b. When trying to determine the y-intercept of a quadratic function, which form is easier to use:

factored form or standard form? Why? Part III: Putting it all together: graph each of the following functions.

• If the function is quadratic, label the x-intercepts, the y-intercept and the vertex.

• If the function is NOT quadratic, simply label the y-intercept.

12. 13.

p(x) = x + 2( ) x + 5( ) q(x) = x −3( ) x + 7( ) r(x) = −3 x + 4( ) x −3( )

h(x) = x +1( ) x + 5( ) g(x) = − x −1( ) x −3( )



14. 15.

16. 17.

k(x) = x +3( ) x −3( ) L(x) = 53x − 4

p(x) = −2 x − 6( ) x + 2( ) r(x) = −x x − 6( )

Algebra 1 – Module 7: Quadratic Functions Name _______________________________ Q – 4.3: Stations Activity Per _____ Date _______________________


Station 1 x-intercepts at ___________________ x-coordinate of the vertex is at x = __________________ The vertex is at ___________________ The y-intercept is at ___________________ Graph: (label the units/scale on each axis)
















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Algebra 1 – Module 7: Quadratic Functions Name...2020/03/27 · b. When trying to determine the y-intercept of a quadratic function, which form is easier to use: factored form or