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Name______________________________ Date _____________
Ctass _____________
For Exercises 1-4, tell whether the graph of the function
a. opens upward or downward
b. has a maximum or minimum
c. is a reflection across the x-axis of the parent function
d. is a stretch or a compression (shrink)?
1. Y = 4x
2
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3. Y = -3 .2x
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4. y
= OAx 2 _5_-+
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tl :?__
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Determine the characteristics of each quadratic function.
6. y = - 2.5x 2
5. y = 1.5x 2 y
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vertex: __
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~______________
Vertex:
C______________
Minim um (if any) : _ __
Maximum (if any):
Minimum (if any):
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0______________
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Maximum (if any) ___
Parent function reflected across x-axis? e
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Solve.
7. A quadraticfunction has the form y = ax 2 for some nonzero value of a
and (4. 48) is on the graph. What is the value of a?
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Original content Copyright © by Hough ton Mifflin Harcourt Addi tions and changes to the original content are the responsibility of the instructor.
76
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Name_____________________________ Dale _ _ _ _ ____ Class _ _ _ _ __
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Transforming Quadratic Functions
Practice and Problem Solving: AlB
A parabola has the equation ((x)
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1. The vertex is
=
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2(x - 3)2 - 4. Complete:
Y. )
2. The graph opens
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3. The function has a minimum value of _______
The following graph is a translation of y = ~. Use it for 4-6 .
4. What is the horizontal translation?
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5. What is the vertical translation?
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6. What is the quadratic equation for the graph
4-tt.... - 4
4-
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Graph the. following parabolas.
7. y= - 2(x+ 1)2+2
( 2
t.,
8. y=2 (X-2/-3
2
--- .
y
y
x
I
C
- 2y
-6
9-12(:.
9. What is the vertex?
c:)
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11. Find two points on either side of the axis.
and
(j.J
7)
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2....
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-- 7
10. What is the axis of symmetry? ____ _ _ _
(4 J 7)
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V e,....,
i r·,X ::=- 4
A ball follows a parabolic path represented by f(x) = -2(x - 5)2 + 9.
Use this equation for
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,-4
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x
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Y
X
4
4
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x
;f
12. Graph the parabola.
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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Name _
_ _ _ _ _ _ __
_ _ _ _ Date _ _ _ _ _ _ Class _ _ _ _ __
Interpreting Vertex Form and Standard Form
Practice and Problem Solving: AlB
Determine if each function is a quadratic function.
1. Y = 2X2 - 3x + 5
3 Y = 2 x + 3x - 4
2. Y = 2x - 4
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Write each quadratic function in standard form and write the equation
for the line of symmetry. I _~
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~,.,.... ,...4. Y =X + 2 + X2
'2(/)
5. Y ='- 1+ 2x- x 2 '
z( - I)
6. --
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J
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rJ ~ - X2.+ 2.,( - I •
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~:-=-I Change the vertex form to standard quadratic form. 7. y= 2(x + 3)2 -6 o;:-2.()('~6x-t-'1)
8. y=3(x - 5)2 + 4
-6
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t- I L
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s) + Lf
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Use the v~lues in the table to Write a quadratic equation in vertex
form , then write the function in standard form .
10. The vertex of the funct ion is (-3 , -2) .
,
9. The vertex of the function is (1, - 3).
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y
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Original cont ent Copyri gh t © by Houghton Mifflin Harcoun . Add itions an d changes to the original content are the responsibility of the instructor
"1-
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Name_______________________________ Dale _____________ Class _____________
11 . The graph of a function in the form
f(x) = a(x - h)2 + k is shown . Use the
graph to find an equation for f(x)
y
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Original conlenl Copyrighl © by Houghlon Mifflin Harcoun . Additions and changes 10 lhe original conlenl are lhe responsibilily of lhe InslrUCIO!.
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