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Unit 3: Exploring Quadratic Equations Study Guide (Due 12/3/25)

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28 questions
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Graphing Quadratic Equations

Question 1
1.
What is the vertex of this parabola? Name the coordinate.
_______
Question 2
2.

What is the axis of symmetry of this quadratic function? It should be in the form of x=h.

Question 3
3.
The quadratic function


has a horizontal shift of ____________________ and a vertical shift of____________________ and is pointed __________ and is being__________
Question 4
4.
Describe the transformation of:


Stretch or Compression?(If a=1 or a=-1, then write none)_______
Opens upward or downward?_______
Horizontal shift? (If there is no shift write none)_______
Vertical shift? (If there is no shift write none)_______
Axis of Symmetry? (x=h)_______
Vertex (h,k)_______
Question 5
5.

Graph this function:


Axis of Symmetry (x=h) -_______

Vertex (h,k)-_______
Question 6
6.

Graph this function:


Axis of Symmetry (x=h) -_______

Vertex (h,k)-_______



Question 7
7.

Graphing Standard Form


What is the graph of the function?


Be sure to include relevant graph detail: use the axis of symmetry and vertex to sketch the graph and use arrows to represent end behavior.

Axis of Symmetry (x=h) -_______

Vertex (h,k)-_______

Connecting Zeros, x-intercepts, and Solutions

Question 8
8.
Guided Practice:
Connecting intercepts and factors

Graph the Function y=(x − 3)(x + 5)

Where does the parabola intercept (cross) the x-axis?
x=_______ and x=_______

How are the intercepts and the factors related to each other?
_______
Question 9
9.
Graph the Function y=(x + 6)(x + 2)



1) What are the x-intercepts? (Where the graph crosses the x-axis)
x=_______ and x=_______
2) What is the axis of symmetry? (The middle of the parabola, put your hands together)
x=_______
Question 10
10.
Graph the function using its intercepts.


What are the coordinates of the x-intercepts?

_______ and _______

What is the axis of symmetry (in the form of x=h)
_______

What is the vertex?
_______
Question 11
11.
Guided Practice: Graphing and Interpreting Quadratic Functions

The height of a football after it has been kicked from the top of a hill can be modeled by the equation:

Where h is the height of the football in feet and t is the time in seconds.

How high does the football get?_______

When is the football at its highest point?_______

How long is the football in the air?_______

Graph the function to answer the question.

Solving Quadratic Equations by Graphing

Question 12
12.
Solve this quadratic equation graphing.
Left Solution
x=_______
Right Solution
x=_______
Question 13
13.
Solve this quadratic equation graphing.
Left solution
x=_______
Right Solution
x=_______
Question 14
14.
A bird is in a tree 30 feet off the ground and drops a twig that lands on a
rosebush 25 feet below. The function h (t) = -16t²+ 30, where t represents the time
in seconds, gives the height h, in feet, of the twig above the ground as it falls. When
will the twig land on the bush?


Solve this quadratic equation graphing.

t=_______

Factoring Quadratics

Question 15
15.

Factor each expression. Be sure to check for a GCF first.

Question 16
16.

Factor each expression. Be sure to check for a GCF first.

Question 17
17.
Factor this standard form quadratic expression.

Use the box method to show your work.

_______ and _______
Question 18
18.
Factor this standard form quadratic expression.


Use the box method to show your work.


_______ and_______

Day 2 12/2/25

Solving Quadratics by Factoring

Question 19
19.
Solve the following Quadratic function:

(x - 7)(x + 7) = 0

x=_______ and x=_______
Question 20
20.
Solve for w


w=_______ and w=_______
Question 21
21.
Solve this standard form quadratic equation. (factor it first, then solve)


x=_______ and x=_______
Question 22
22.
Solve this standard form quadratic equation. (factor it first, then solve)



x=_______ and x=_______
Question 23
23.
Solve this standard form quadratic equation. (factor it first, then solve)



x= _______ and x=_______
Question 24
24.
Solve this standard form quadratic equation.



x=_______ and x=_______


Question 25
25.
Solve this standard form quadratic equation.



x=_______ and x=_______

Solving Quadratics Using Square Roots

Question 26
26.
Solve this quadratic equation.


x=_______ and x=_______
Question 27
27.
Solve this quadratic equation.




x=_______ and x=_______

Quadratic Word Problems

Question 28
28.
Write and solve the equation describing the relationship:

Find the length and width of a rectangle whose length is 5 cm longer than its width and whose area is 50 cm².

Write the equation that represents: "length is 5 cm longer than its width"
_______


What is the length?
_______
What is the width?
_______