Unit 6 Quadratic Functions
Math II
Mini Lesson:
Domain and Range
Recall that a set of ordered pairs is also called a relation.
The domain is the set of x-coordinates of the ordered pairs.
The range is the set of y-coordinates of the ordered pairs.
Interval Notation is the way to represent the domain and range of a function as an
interval pair of numbers.
–Examples: [-2, 3], (0, 2], (-∞, ∞)
–The numbers are the end points of the interval
–Use parenthesis if the endpoint is NOT included
–Use brackets if the endpoint IS included
– ∞ (Infinity) : Use this if numbers go on forever in the positive direction
– -∞ (Negative Infinity) : Use this if numbers go on forever in the negative direction
Introduction to Domain and Range
Domain and Range from Graphs
y
Find the domain and
range of the function
graphed to the right.
Use interval notation.
x
Domain: [ -3, 4 ]
Range: [ -4, 2 ]
Introduction to Domain and Range
Domain and Range from Graphs
y
Find the domain and
range of the function
graphed to the right.
Use interval notation.
x
Domain: ( -∞, ∞ )
Range: [ -2, ∞ )
Introduction to Domain and Range
Write the domain and range in interval notation.
Domain:
Range:
Introduction to Domain and Range
Write the domain and range in interval notation.
Domain:
Range:
Introduction to Domain and Range
Write the domain and range in interval notation.
Domain:
Range:
Introduction to Domain and Range
Write the domain and range in interval notation.
Domain:
Range:
Introduction to Domain and Range
Write the domain and range in interval notation.
Domain:
Range:
Introduction to Domain and Range
Write the domain and range in interval notation.
Domain:
Range:
Introduction to Domain and Range
Write the domain and range in interval notation.
Domain:
Range:
Introduction to Domain and Range
Write the domain and range in interval notation.
Domain:
Range:
Introduction to Domain and Range
Domain and Range worksheet!
Find the Domain and Range of each graph.
Whoever can finish 1st, 2nd, and 3rd with all
questions correct will get a piece of candy! 
Introduction to Quadratic Functions
• A quadratic function always has a degree of 2.
– This means there will always be an x2 in the equation and never
any higher power of x.
• The shape of a quadratic function’s graph is called a
parabola.
- It looks like a “U”
• The Standard Form of a Quadratic is
y = ax2 + bx + c
Where a, b, and c can be real numbers with a ≠ 0.
Introduction to Quadratic Functions
Most Basic Quadratic Function:
y = x2
Axis of
Symmetry
Domain: (-∞,∞∞)
Range: [0, ∞)
Vertex
Introduction to Quadratic Functions
X-Intercepts
Roots
Zeroes
Solutions
Quadratic vocabulary
-Axis of Symmetry – the line that divides a parabola into 2 parts that
are mirror images. The axis of symmetry is always
a vertical line defined by the x-coordinate of the
vertex. (ex: x = 0)
-Vertex – the point at where the parabola intersects that axis of
symmetry. The y-value of the parabola represents the
maximum or minimum value of the function.
-X-Intercepts, Zeroes, Roots, Solutions – All of these terms mean the
same thing and refer to where the parabola crosses the x-axis.
When asked to solve a quadratic, this is what we are looking
for!
-Minimum – If the graph opens up (smiles) and the vertex is the lowest point on the
graph, then the vertex is a minimum.
-Maximum - If the graph open down (frowns) and the vertex is the highest point on the
graph, then the vertex is a maximum.
Example:
Find the vertex, axis of symmetry, zeroes, and domain and range of the
quadratic function. Determine if the vertex is a minimum or a maximum.
Vertex:
Axis of Symmetry:
Zeroes:
Domain:
Range:
Min or Max?:
Vertex:
Axis of Symmetry:
Zeroes:
Domain:
Range:
Min or Max?:
Back to Standard Form!
y = ax2 + bx + c
-If a > 0, then vertex will be a minimum.
-If a < 0, then vertex will be a maximum.
-If in standard form, use the formula
of symmetry.
b
x
2a
to find axis
– This will also be the x coordinate of the vertex, substitute that into the
original equation to find the y coordinate.

Example: Put each in Standard Form. Determine whether each
function is a quadratic.
1. f(x) = (-5x – 4)(-5x – 4)
1. y = 3(x – 1) + 3
1. y = x2 + 24 – 11x – x2
1. f(x) = 3x(x + 1) – x
1. y = 2(x + 2)2 – 2x2
Example: Determine whether the vertex will be a maximum or
minimum. Find the Axis of Symmetry and Vertex of
each.
1. y = x2 – 4x + 7
1. y = -3x2 + 6x - 9
1. y = 2x2 – 8x + 1
1. y = -x2 – 8x – 15
Finding Quadratic Models!
(in your calculator)
Find a quadratic model for a set of values.
-Step 1: Enter the data into the calculator (STAT -> Edit)
(x’s in L1, y’s in L2)
-Step 2: Calculate the Quadratic Regression model by hitting
STAT again  Calc, then 5: QuadReg
-Step 3: Substitute the given a, b, and c values into the
standard form.
Example: Find a quadratic model for each set of values.
1. (1, -2), (2, -2), (3, -4)
2.
x
f(x)
-1
-1
1
3
3
8
Quadratic Model Application
A man throws a ball off the top of a building. The table
shows the height of the ball at different times.
Height of a Ball
Time
Height
0s
46 ft
1s
63 ft
2s
48 ft
3s
1 ft
a. Find a quadratic model for the data.
b. Use the model to estimate the height of the ball at
2.5 seconds.