Name:_________________________________
Review: Sections 2.1-2.5
STANDARD FORM of a Quadratic: ______________________________
Vertex: (
,
Finding zeros:
)
Axis of symmetry: ______
(MEMORIZE)
x-intercepts: zeros/roots/solutions
Degree 2: In standard form: Set f(x) to zero and solve by using square roots (Remember ±)
Not in standard form: factor and solve for x. If you cannot factor, use quadratic formula! (memorize)
Higher than degree 2: Set f(x) to zero and try to factor by GCF or grouping.
If it cannot factor, must use rational zero test.
GRAPH THE FOLLOWING.
1) y =2(x + 1)2 - 4
Vertex:_________
Axis of Symmetry:
___________
x-intercept(s): _______________
2) y = x2 – 6x + 7 (Get into standard form!)
Standard Form: ___________________ Vertex:_________
Axis of Symmetry:
___________
x-intercept(s): _______________
3) Write an equation in standard form that has a vertex (3, 6) and goes through the point (1, -2).
4) The path of a diver is given by the equation y= -2x2 + 20x – 46 where y is the height (in feet) and x is the
horizontal distance from the end of the diving board. What is the maximum height of the diver?
Write the following in standard form and identify the vertex. (Hint What process should you do!?)
5) y = x2 + 12x – 39
6) y = 3x2 + 24x + 49
7) y = -2x2 + 4x + 3
f(x) = ___________________
f(x) = ___________________
f(x) = ___________________
Vertex:_________
Vertex:_________
Vertex:_________
GRAPH THE FOLLOWING POLYNOMIALS BY HAND.
9) f(x) = 2x3 – 2x2 – 12x
8) f(x) = - x4 + 9x2
Zeros:________
Zeros:________
y-int:_________
y-int:_________
FIND THE ZEROS. Do NOT use completing the square.
10) f(x) = 2x3 + x2 – 72x – 36
11) f(x) = x2 – 4x + 5
12) Use the chart to determine where there is/are a root(s)
______________________________________________________
x -2
y -4
-1
2
0 1
3 5
2
-2
3
-1
WRITE AN EQUATION WITH THE GIVEN ROOTS.
13) 0 (double root), -7, 7
14)  3i, -6, 2
WRITE THE EQUATION OF EACH GRAPH.
Answer:______________________________
Answer:_______________________________
15)
16)
COMPLETE THE FOLLOWING. SHOW ALL WORK!
17) Use the Remainder Theorem to determine if (x – 3)
is a factor of (2x4 + 9x3 – 9x2 – 46x + 24)?
17.
YES or
NO
18) Is –2 a root of x4 + 5x2 – 36? Support!
18.
YES or
NO
19) Divide (x4 + x3 – 2x2 + 4x – 24) by (x – 2)
and name the remaining polynomial
19.
__________________
20) Find the value of k so that the remainder is 0.
(3x3 + 6x2 – kx – 9) ÷ (x + 3)
20.
k = ______________
21. y = x3 – 2x2 - 4x + 8
number of complex roots:
number of possible positive roots:
number of possible negative roots:
Is –1 a root?
Is 1 a root?
possible roots:
factors of
factors of


Zeros:_____________ y-int:_______
22.
y = 4x4 – 12x3 + 3x2 + 13x – 6
number of possible positive roots:
number of complex roots:
number of possible negative roots:
Is –1 a root?
Is 1 a root?
possible roots:
factors of
factors of


Zeros:_____________ y-int:_______
23) The path of a football is represented by the equation y = -(x – 2)2 + 10 where x represents time in seconds and y
represents the position in feet.
a) After how many seconds has the football reached its maximum height?
b) What is the maximum height?
c) At what position does the object begin its path?