Algebra 18 - Chapter 10 - Part 1
IDate
Assigned
Day
Mathlete:
Topic
Homework
(due the next day)
Thu
1/12
1
Intro to Quadratic Functions and
Graphing Part 1
Intro to Quadratic Functions and Graphing
Worksheet 1
Fri
1/13
2
Intro to Quadratic Functions and
Graphing Part 2
Intro to Quadratic Functions and Graphing
Worksheet 2
Tue
1/17
3
Solving Quadratics by Factoring and
Taking Square Roots
Solving Quadratics by Factoring and Taking
Square Roots Worksheet
Wed
1/18
4
Review: Graphing Quadratic
Functions using Intercepts
Graphing Quadratic Functions using Intercepts Part 2
Thu
1/19
Quiz on days 1-4
Mon 1/16 - MLK no school
I
Name:
Hour:
Algebra 1: Intro to Quadratic Functions and Graphing Part 1
Use the link below for the Quadratic Explorer to investigate graphs of quadratic functions.
Fill in the blanks using the function y = ax2 + bx + c .
http://mathopenref.com/quadraticexplorer.html
The maximum or minimum is called the
The line of reflection is called the
The y-intercept is (0,
).
The y-intercept is not affected by
or
The x-coordinate of the vertex is affected by
The graph opens up if
and
, but not by
and the graph opens down if
If the graph opens up, then there is a
If the graph opens down, then there is a
As the absolute value of "a" gets larger, the graph becomes
As the absolute value of "a" gets smaller, the graph becomes
To find the equation for the
take the average of the x-coordinates of two
x-intercepts (or any two points with the same y-coordinate).
If you substitute this x — coordinate into the original equation, you will find the y — coordinate of the
Example: Use the function y = x2 — 2x —3 to answer the questions and fill in the blanks.
Then graph the function by creating a table of values.
Does the graph open up or down?
Does the graph have a maximum or minimum?
Is the graph wider or narrower than the graph of y = 4x2 —5?
What is the y-intercept?
What is the equation of the axis of symmetry?
What are the coordinates of the vertex?
X
x2
-2x -3
y
2
—1
0
1
2
3
Example: Use the function y = —2x2 +18 to answer the questions and fill in the blanks.
Then graph the function by creating a table of values.
Does the graph open up or down?
Does the graph have a maximum or minimum?
Is the graph wider or narrower than the graph of y = 0.25x2 —3x + 8?
What is the y-intercept?
What is the equation of the axis of symmetry?
What are the coordinates of the vertex?
x
—2
—1
0
1
2
3
—2x2 +18
4
Name:
Hour:
Algebra 1: Intro to Quadratic Functions and Graphing Worksheet 1
1. Use the function y = X2 - X - 2 to answer the questions and fill in the blanks.
Then graph the function by creating a table of values.
Does the graph open up or down?
Does the graph have a maximum or minimum?
Is the graph wider or narrower than the graph of y = 3x2 — 2x + 5?
What is the y-intercept?
A
What is the equation of the axis of symmetry?
What are the coordinates of the vertex?
—2
—1
0
1
I
2
2. Use the function y = —x2 + x + 6 to answer the questions and fill in the blanks.„
Then graph the function by creating a table of values.
Does the graph open up or down?
Does the graph have a maximum or minimum?
Is the graph wider or narrower than the graph of y = 0.5x2 + 5x?
What is the y-intercept?
What is the equation of the axis of symmetry?
What are the coordinates of the vertex?
—
—2
—1
1
2
+x+6
3. Use the function y = 2x2 — 6x + 4 to answer the questions and fill in the blanks.
Then graph the function by creating a table of values.
Does the graph open up or down?
Does the graph have a maximum or minimum?
Is the graph wider or narrower than the graph of y = x 2 + 3 ?
What is the y-intercept?
What is the equation of the axis of symmetry?
What are the coordinates of the vertex?
2
X
x+4
—2
—1
0
1
2
1 2
4. Use the function y = — x - X - 4 to answer the questions and fill in the blanks.
2
Then graph the function by creating a table of values.
Does the graph open up or down?
Does the graph have a maximum or minimum?
Is the graph wider or narrower than the graph of y = x2 — 3x + 9?
What is the y-intercept?
What is the equation of the axis of symmetry?
What are the coordinates of the vertex?
x
—2
—1
0
1
2
"
—x
Name:
Hour:
Algebra 1: Intro to Quadratic Functions and Graphing Part 2
and solve for
To find the y-intercept, plug in
To find the x-intercept(s), plug in
and solve for
3
•
Example: Graph y = — x —6 by finding the x-intercept and y-intercept.
2
Find the y-intercept:
Find the x-intercept:
Example: Graph y = x2 — 2x —3 by finding the x-intercept(s) and y-intercept.
Does the graph open up or down?
Find the y-intercept:
Find the x-intercept(s):
Find the axis of symmetry:
Find the vertex:
Zero-Product Property
If a • b = 0 , then a = 0 or b= 0,
What is x if 4. x = 0 ?
Example: Graph y = x2 + 3x —4 by finding the x-intercept(s) and y-intercept.
Does the graph open up or down?
Find the y-intercept:
Find the x-intercept(s):
.1
Find the axis of symmetry:
Find the vertex:
Example: Graph y = —x2 — 6x - 9 by finding the x-intercept(s) and y-intercept.
Does the graph open up or down?
Find the y-intercept:
Find the x-intercept(s):
4,-.
Find the axis of symmetry:
Find the vertex:
Example: Graph y = x2 - 25 by finding the x-intercept(s) and y-intercept.
Does the graph open up or down?
Find the y-intercept:
Find the x-intercept(s):
,
Find the axis of symmetry:
Find the vertex:
Example: Graph y = 2x2 —12x by finding the x-intercept(s) and y-intercept.
Does the graph open up or down?
Find the y-intercept:
Find the x-intercept(s):
4
Find the axis of symmetry:
Find the vertex:
Name:
Hour:
Algebra I: Intro to Quadratic Functions and Graphing Worksheet 2
1. y = x2 + 3x — 28
2. y = 2x2 — 5x — 3
Does the graph open up or down?
Does the graph open up or down?
Find the y-intercept:
Find the y-intercept:
Find the x-intercept(s):
Find the x-intercept(s):
Find the axis of symmetry:
Find the axis of symmetry:
Find the vertex:
Find the vertex:
3. y =x2 —3x-10
4. y = x2 —4x+ 4
Does the graph open up or down?
Does the graph open up or down?
Find the y-intercept:
Find the y-intercept:
Find the x-intercept(s):
Find the x-intercept(s):
Find the axis of symmetry:
Find the axis of symmetry:
Find the vertex:
Find the vertex:
5. y = x2 +2x
6. y---x2 +x+6
Does the graph open up or down?
Does the graph open up or down?
Find the y-intercept:
Find the y-intercept:
Find the x-intercept(s):
Find the x-intercept(s):
Find the axis of symmetry:
Find the axis of symmetry:
Find the vertex:
Find the vertex:
A
A
r
r
7. y = 4x2 +12x-7
8. y = x2 — 9
Does the graph open up or down?
Does the graph open up or down?
Find the y-intercept:
Find the y-intercept:
Find the x-intercept(s):
Find the x-intercept(s):
Find the axis of symmetry:
Find the axis of symmetry:
Find the vertex:
Find the vertex:
Name:
Hour:
Algebra 1: Solving Quadratics by Factoring and Taking Square Roots
We can use the zero-product property to solve quadratic equations by factoring.
The equation must be set equal to zero to use this property.
Solve by factoring.
1. x2 —2x —63 = 0
2. x2 —7x = 30
3. x2 +8x+7=-5
4. 3x2 +9x = 0
5. (x+4)(2x-7)=
6. 7x2 —15x+3 =x2 —4x
We can solve quadratic equations by taking the square root of each side if b = 0.
Note that when b = 0, there is no middle term.
To solve by taking the square root of each side, you must first get x2 by itself on one side.
Solve by taking the square root of each side.
7. x2 = 81
8. x2 —5 = 2
9. --5x2 =25
10. —3x2 = —27
11. x2 +17 =17
12. 3x2 +15 = 63
13. 5x2 —13 = 32
14. 2 —3x2 = —10
Name:
Hour:
Algebra 1: Solving Quadratics by Factoring and Taking Square Roots Worksheet
Solve by factoring.
1.
+ 2x —15 = 0
3. x2 +8x = —15
2. x2 —11x+19 =-5
4. 7x2 +2x =0
Solve by taking square roots.
5. x2 = 36
6. x2 +5=8
7. 16x2 = 49
8. 2x2 +10 =210
Solve each equation.
9. 7x2 = —21
10. 7x2 -6x+3=3
11. (4x+5)(x+0= 0
12. x2 —5 = —5
13. 3— 4x2 =-61
14. 7x2 —14x = —7
15. 5x2 -44x+120 =-30+11x
16. 4x2 —11= —2
Name:
Hour:
Graphing Quadratic Functions using Intercepts
1. y = x2 + 4x — 5
2. y = —x2 —4x-3
Does the graph open up or down?
Does the graph open up or down?
Find the y-intercept:
Find the y-intercept:
Find the x-intercept(s):
Find the x-intercept(s):
Find the axis of symmetry:
Find the axis of symmetry:
Find the vertex:
Find the vertex:
3. y = X2 + X - 6
4. y = 2x2 + 8x + 8
Does the graph open up or down?
Does the graph open up or down?
Find the y-intercept:
Find the y-intercept:
Find the x-intercept(s):
Find the x-intercept(s):
Find the axis of symmetry:
Find the axis of symmetry:
Find the vertex:
Find the vertex:
5. y = —3x2 —6x
6. y = —x2 +6x —8
Does the graph open up or down?
Does the graph open up or down?
Find the y-intercept:
Find the y-intercept:
Find the x-intercept(s):
Find the x-intercept(s):
Find the axis of symmetry:
Find the axis of symmetry:
Find the vertex:
Find the vertex:
A
r.
.
7. y = 2x2 +7x —4
8. y = 4x2 —9
Does the graph open up or down?
Does the graph open up or down?
Find the y-intercept:
Find the y-intercept:
Find the x-intercept(s):
Find the x-intercept(s):
Find the axis of symmetry:
Find the axis of symmetry:
Find the vertex:
Find the vertex:
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Name:
Hour:
Graphing Quadratic Functions using Intercepts — Part 2
1. y = —4x2 + 25
2. y = 2x2 — 4x —30
Does the graph open up or down?
Does the graph open up or down?
Find the y-intercept:
Find the y-intercept:
Find the x-intercept(s):
Find the x-intercept(s):
Find the axis of symmetry:
Find the axis of symmetry:
Find the vertex:
Find the vertex:
3. y =x2 —10x+9
4. y
Des the graph open up or down?
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64
Does the graph open up or down?
Find the y-intercept:
Find the y-intercept:
Find the x-intercept(s):
Find the x-intercept(s):
Find the axis of symmetry:
Find the axis of symmetry:
Find the vertex:
Find the vertex:
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5. y = —x2 — 8x
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Does the graph open up or down?
Does the graph open up or down?
Find the y-intercept:
Find the y-intercept:
Find the x-intercept(s):
Find the x-intercept(s):
Find the axis of symmetry:
Find the axis of symmetry:
Find the vertex:
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7. y = 9x2 —36
8. y = —x2 —6x —9
Does the graph open up or down?
Does the graph open up or down?
Find the y-intercept:
Find the y-intercept:
Find the x-intercept(s):
Find the x-intercept(s):
Find the axis of symmetry:
Find the axis of symmetry:
Find the vertex:
Find the vertex:
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