Download XEI 605 Solve quadratic equations

CW#18H: Compare Quadratic Functions &
Solve by Graphing
Honors Geometry
Name: _____________________________ TP: ____
CRS
Objectives
Algebra Content
XEI 605 Solve quadratic equations
4.3 Compare quadratic graphs in form y =ax2 + c with the parent quadratic function
4.4 Solve quadratic equations by graphing y = ax2 + bx + c
y =ax2 + c
Transformations
-
Quadratic functions can __________________ ( narrow) or ___________________ (wide)
-
Shift ___________ or ___________
-
Reflect on the __________________________
Stretch (narrow)
Shrink (wide)
Shift up
Shift down
Reflection (sad
face)
1) Which multiple choice option describes the correct
transformation to the parent graph (
)?
2) How would the graph of the function y = x2 + 4
affected if the function were changed to y = x2 – 3?
A. Shrink and shift down 1 units
B. Stretch and shift down 3 units
C. Stretch and reflection across the x-axis
D. Shrink, shift down 3 units, and reflection
across the x-axis
E. Shrink and reflection across the x-axis
A. The graph would shift 4 units up.
B. The graph would shift 3 units down.
C. The graph would shift 7 units down.
D. The graph would shift 4 units to the right.
E. The graph would shift 4 units down.
3) Describe the transformation of y = 5x2 – 4 to the
parent function?
4) How would the graph of the function
y = x2 -2 affected if the function were changed to y =
x2 + 4?
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5) Which multiple choice option describes the correct
transformation to the parent graph (
)?
6) How would the graph of the function y = x2 – 2
affected if the function were changed to y = x2 + 1?
A. Shrink and shift up 5 units
B. Stretch and shift up 5 units
C. Stretch and reflection across the x-axis
D. Shrink, shift up 5 units, and reflection
across the x-axis
E. Stretch, shift up 5 units, and reflection across the xaxis
7) Describe the transformation of y = -x2 + 7 to the
parent function?
A. The graph would shift 1 unit up.
B. The graph would shift 2 units down.
C. The graph would shift 3 units down.
D. The graph would shift 3 units to the right.
E. The graph would shift 3 units up.
9) Describe the transformation of y = -2x2 – 4 to the
parent function?
10) How would the graph of the function
y = x2 – 6 affected if the function were changed to
y = x2+ 2?
11) Describe the transformation of y = 6x2 + 8 to the
parent function?
12) How would the graph of the function
y = x2 + 1 affected if the function were changed to
y = x2+ 5?
8) How would the graph of the function
y = x2 + 2 affected if the function were changed to y =
x2 – 5?
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Question: How do I solve quadratic equations by graphing?
Step 1: Write the equation in standard form: _________________________
Step 2: Graph the function (following the steps from yesterday) to determine the __ - _______________. These
values are called the “_________” or “_________” of a function, and are the solutions to the function.
Quadratic Equation with TWO
Quadratic Equation with ONE
Quadratic equation with NO real
solutions must have ___
solution must have ____
solution must have ___
x-intercepts.
x-intercept.
x-intercepts.
Step 3: If solutions are found, check the solutions by substituting them into the ___________ _____________.
1) Solve x 2  2x  3 by graphing.
a. Table:
x
2) Find the zeros of the function: f (x)  x 2  2x  1
b. Graph:
a. Table:
y
x
c. AOS:
b. Graph:

y
d. Vertex: ( ___ , ___ )
circle one: max min c. AOS:
d. Vertex: ( ___ , ___ )
circle one: max min
e. Solutions: ___________________________
e. Solutions: ___________________________
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2
3) Find the roots of x  7  4 x .
a. Table:
x
c. AOS:
4) Solve the equation by graphing. Label the vertex
and axis of symmetry.
b. Graph:
y 
d. Vertex: ( ___ , ___ )
circle one: max min
e. Solutions: ___________________________
5) What are the roots of the function  x 2  2 x  3 ?
Label the vertex and axis of symmetry.
6) How many solutions does the quadratic equation
have? Label the vertex and
axis of symmetry.
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7) The graph y  x 2  4 x  5 is shown below.
Which choice best describes the solution(s) to this
equation?
8) The graph of y  x 2  2x  3 is shown below. For
what values of x does y  0 ?






A.
B.
C.
D.
x  5
x 5
x 1
Both A and C


9) Use the graph to find the solution to the equation

11) Solve the equation by graphing. Label the vertex
and axis of symmetry.
A.
B.
C.
D.

x  1 and x  0
x  1 and x  3
x  3 and x 1
x 1 and x  3
10) Use the graph to find the solution to the equation
12) Solve the equation by graphing. Label the vertex
and axis of symmetry.
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EXIT SLIP:
1) Find the zeros, if any, of  2 x 2  x  3 .
a. Table:
x
c. AOS:
NAME: ____________________________
2) Describe the transformation of y = -½x2 – 1 to the
parent function?
b. Graph:
y
d. Vertex: ( ___ , ___ )
circle one: max min
e. Solutions: ___________________________
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