# Algebra II – Problem Set Unit 3 Quadratic Functions

```Algebra II – Problem Set
Name:____________________
Block:______________
1) For each of the following, write the form of the equation for the quadratic function and then explain
how to graph the function from that particular equation.
a) Standard Form:_____________________________________
b) Vertex Form:_______________________________________
c) Intercept Form:______________________________________
2) Graph each of the following and label the vertex, axis of symmetry, and zeros.
1
2
a ) f ( x)  2  x  3  5
c) y   x  4  x  2 
b) g ( x)  2 x 2  6 x  5
2
3) Factor each of the following completely.
a) x 2  8x  16
b) 7 x 2  11x  6
d ) 9 x 2  12 x  4
e) 81a 2  25
c) 5x 2  11x  12
f ) x 2  29 x  54
4) Write the function in vertex form. Then, identify the vertex and axis of symmetry.
f ( x)  x 2  12 x  20
5) Write the function in standard form. f ( x)  2  x  3  5
2
6) Find the discriminant and determine the nature of the roots for the function g ( x)  4 x 2  3x  2 .
7) Select all of the following that have two distinct real roots:
a) y  6 x 2  2 x  3
b) f ( x)  9 x 2  3x  2
c) g ( x)  2 x 2  8x  8
d) h( x)  5x 2  x  4
e) y  x 2  6 x  9
f) k ( x)  4 x 2  4 x  5
8) Write the equation of each graph shown in both intercept and vertex forms.
a)
b)
9) Select all of the following functions which have no real solutions.
A)
B)
C)
D)
E)
F)
10) Give an example of a real-world situation that is modeled by a quadratic function.
11) Describe the transformation of the equation f ( x)    x  5   3 compared to its parent function
2
f ( x)  x 2 .
12) Write the equation given graphical transformations of a downward shift of 1, a right shift of 6 and a
stretch (narrow) of 2.
2
13) GRAPH: y= -x - 6x - 5
What is the vertex?________________________
What is the y-intercept?:_______________
What is the axis of symmetry? _______________
What is the domain?_______________________
What is the range?:_________________________
What is the max or minimum point? ___________________
How many roots are there?________________
What are the solutions of this equation? __________________
What do you call these solutions? _____________________
Where is the graph increasing?:_______________________
Where is the graph decreasing?:_______________________
```