Quadratic Basics LESSON

​Attributes of a Quadratic

• Answer the questions as best as you can.

• You are expected to get a few wrong at the beginning and then do better once you figure it out towards the end.

• Write the definitions on given notes handout

• Write your answers for each graph, answers are ordered pairs like (4,2)

LEAVE THIS GRAPH Blank

We will complete together the following day.

Multiple Choice

Which letter represents the y-intercept?

• A

• B

• C

• D

Y-intercept of a graph

Where the parabola crosses the y- axis.

Multiple Choice

What is the ordered pair of the y-intercept?

Write the answer down for Graph 1 on your notes.

• $$\left(-4.5,\ 0\right)$$

• $$\left(0,-1\right)$$

• $$\left(-2,\ -3\right)$$

• $$\left(0.5,\ 0\right)$$

Multiple Choice

Which letter represents the POSITIVE x-intercept?

• A

• B

• C

• D

Multiple Choice

Which letter represents the NEGATIVE x-intercept?

• A

• B

• C

• D

Multiple Choice

What are the ordered pairs of the x-intercepts?

Write these answers down on Graph 1

• $$\left(-4.5,\ 0\right)$$ $$\left(0.5,\ 0\right)$$

• $$\left(0,-1\right)$$ $$\left(-2,-3\right)$$

• $$\left(-2,\ -3\right)$$ $$\left(0.5,\ 0\right)$$

• $$\left(0.5,\ 0\right)$$ $$\left(-3,-2\right)$$

x-intercept of a graph

Where the parabola crosses the x-axis.

A parabola can have 2, 1, or no x-intercepts at all.

x-intercepts of a Parabola has 3 other names

X-intercepts are called ZEROS, ROOTS, & SOLUTIONS



** Be sure to write this down on your notes **

Multiple Choice

Which letter represents the POSITIVE zero?

• A

• B

• C

• D

Multiple Choice

Which letter represents the POSITIVE root?

• A

• B

• C

• D

Multiple Choice

Which letter represents the POSTITIVE solution?

• A

• B

• C

• D

x-intercepts of a Parabola has 3 other names

X-intercepts are called ZEROS, ROOTS, & SOLUTIONS


Did you write this definition down in your notes ?

Multiple Choice

Which letter do you think represents the VERTEX ?

• A

• B

• C

• D

Vertex of a Parabola

It is the lowest or highest point of the parabola, its located where the parabola curves.



** Be sure to WRITE THIS DOWN in your notes *

Multiple Choice

What is the ordered pair of the VERTEX ?

Write this answer down for Graph 1.

• $$\left(0.5,0\right)$$

• $$\left(-2,-3\right)$$

• $$\left(-3,-2\right)$$

• $$\left(0,-1\right)$$

Multiple Choice

Do you think the vertex is a Minimum Point or Maximum point?

Circle answer on GRAPH 1 of your notes.

• Minimum

• Maximum

Vertex is a Maximum or a Minimum

The vertex is considered to be a MINIMUM when it is the LOWEST point of the parabola.

The vertex is considered to be a MAXIMUM when it is the HIGHEST point of the parabola

** Be sure to WRITE THIS DOWN in your notes *

Multiple Choice

What do you think the range is ?

Write the answer down on GRAPH 1 of your notes.

• $$y\ \ge-3$$

• $$y\le-3$$

Range depends on the Vertex

Multiple Choice

What do you think the DOMAIN is ?

Write the answer down on GRAPH 1 of your notes.

• $$-7\le x\le3$$

• All Real numbers

Domain

The domain of ANY parabola with 2 ARROWS will always be ALL REAL NUMBERS

It does not matter which way the parabola opens.

Multiple Choice

Through which point do you think the axis of symmetry (AOS) goes through?

• A

• B

• C

• D

Axis of Symmetry (AOS)

The axis of symmetry is an imaginary VERTICAL LINE that goes through the vertex and cuts the parabola in half.

The equation of the vertical line is x = #.

The # being the x-value of the vertex.


** Be sure to WRITE THIS DOWN in your notes *

Multiple Choice

Which do you think is the EQUATION of the Axis of Symmetry (AOS) of the parabola?

Write your answer down on graph 1 of your notes.

• $$x=-2$$

• $$x\ =\ -3$$

• $$y\ =\ -\ 2$$

• $$x\ =\ -1$$

Multiple Choice

What is the y-intercept of the parabola?

• A (0 , -6)

• B (2, 0)

• C (4, 2)

• D (6, 0)

Multiple Choice

What is the LARGEST solution value of the parabola?

Write the answer down on GRAPH 2 of your notes.

• Point A

  x = 0

• Point B

  x = 2

• Point C

  x = 4

• Point D

  x = 6

Multiple Choice

What is the SMALLEST solution value of the parabola?

Write the answer down on GRAPH 2 of your notes

• Point A

  x = 0

• Point B

  x = 2

• Point C

  x = 4

• Point D

  x = 6

x-intercepts of a Parabola has 3 other names

X-intercepts are called ZEROS, ROOTS, & SOLUTIONS

Multiple Choice

What is the VERTEX of the parabola?

Write down the ordered pair for the point for GRAPH 2 on your notes.

• A

• B

• C

• D

Vertex of a Parabola

It is the lowest or highest point of the parabola, its located where the parabola curves.

Multiple Choice

What is the RANGE of the parabola?

Write the answer on GRAPH 2 of your notes.

• $$y\le2$$

• $$y\ge2$$

Multiple Choice

Is the vertex of the parabola a maximum or minimum point?

Circle the answer on GRAPH 2 of your notes.

• Maximum

• Minimum

Multiple Choice

What is the equation of the axis of symmetry (AOS) of the parabola?

Be sure to write the answer down on GRAPH 2 of your notes.

• $$x=\ 4$$

• $$x=2$$

• $$y\ =-6$$

• $$x=6$$

Axis of Symmetry

The axis of symmetry is an imaginary VERTICAL LINE that goes through the vertex and cuts the parabola in half.

The equation of the vertical line is x = #.

The # being the x-value of the vertex.

Multiple Choice

What is the equation of the axis of symmetry (AOS) of the parabola?

Write the answer down on Graph 3 of your notes.

• $$x=\ 3$$

• $$x=4$$

• $$y\ =-6$$

• $$x=6$$

Multiple Choice

What letter is the VERTEX of the parabola?

• A

• B

• C

• D

Multiple Choice

Is the vertex a Minimum or Maximum

Circle your answer on GRAPH 3 of your notes

• Minimum

• Maximum

Multiple Choice

What is the range of the graph?

Write your answer down on GRAPH 3 of your notes

• $$y\ge4$$

• $$y\le4$$

Multiple Choice

What is the DOMAIN of the graph?

Write your answer down on GRAPH 3 of your notes

• $$-2\le x\le8$$

• All Real numbers

Multiple Choice

What is the ordered pair of the Vertex?

Write down your answer on GRAPH 3 of your notes.

• $$\left(3,\ 4\right)$$

• $$\left(4,\ 3\right)$$

• $$\left(0,\ 6\ \right)$$

• $$\left(5,\ 5\right)$$

Multiple Choice

What letter is the Y-INTERCEPT of the parabola?

• A

• B

• C

• D

Multiple Choice

What is the ordered pair of the y-intercept?

Write down the answer on GRAPH 3 of your notes.

• $$\left(3,\ 4\right)$$

• $$\left(6,\ 0\right)$$

• $$\left(0,\ 6\ \right)$$

• $$\left(5,\ 5\right)$$

Multiple Choice

How many zeros does the parabola have?

• 1

• 2

• 3

• None

x-intercept of a graph

Where the parabola crosses the x-axis.

A parabola can have 2, 1, or no x-intercepts at all.

Multiple Choice

Is the vertex a Minimum or Maximum ?

Write circle the answer on GRAPH 4 of your notes.

• Minimum

• Maximum

Multiple Choice

What is the RANGE of the parabola ?

Write the answer on GRAPH 4 of your notes.

• $$y\le0$$

• $$y\ge0$$

Multiple Choice

What is the DOMAIN of the parabola ?

Write the answer on GRAPH 4 of your notes.

• All real numbers

• $$-2\le x\le11$$

Multiple Choice

What is the vertex of the parabola?

Write down the answer on GRAPH 4 of your notes.

• $$\left(5,0\right)$$

• $$\left(0,5\right)$$

• $$\left(0,-6\right)$$

• $$\left(-6,0\right)$$

Multiple Choice

What is the y-intercept of the parabola?

Write down the answer on GRAPH 4 of your notes.

• $$\left(5,0\right)$$

• $$\left(0,5\right)$$

• $$\left(0,-6\right)$$

• $$\left(-6,0\right)$$

Multiple Choice

How many x-intercepts does the parabola have?

• 1

• 2

• 3

• none

Multiple Choice

What is the root of the parabola?

Write down the answer on GRAPH 4 of your notes.

• $$\left(5,0\right)$$

• $$\left(0,5\right)$$

• $$\left(0,-6\right)$$

• $$\left(-6,0\right)$$

x-intercepts of a Parabola has 3 other names

X-intercepts are called ZEROS, ROOTS, & SOLUTIONS

Sometimes it is the same as the vertex

Multiple Choice

What is the equation of the axis of symmetry (AOS) of the parabola?

Write down the answer on GRAPH 4 of your notes.

• $$x=5$$

• $$x=-6$$

• $$y=-6$$

• $$\left(-6,0\right)$$

Multiple Choice

Is the vertex a maximum or minimum point?

Circle the answer on GRAPH 5 of your notes.

• Maximum

• Minimum

Multiple Choice

What is the RANGE of the graph?

Write the answer on GRAPH 5 of your notes.

• $$y\le-2$$

• $$y\ge-2$$

Multiple Choice

What is the ordered pair for the VERTEX of the parabola?

Write the answer on GRAPH 5 of your notes.

• $$\left(0,-8\right)$$

• $$\left(-2,5\right)$$

• $$\left(5,-2\right)$$

• $$\left(3,-3\right)$$

Multiple Choice

What is the ordered pair for the y-intercept of the parabola?

Write the answer on GRAPH 5 of your notes.

• $$\left(0,-8\right)$$

• $$\left(-2,5\right)$$

• $$\left(5,-2\right)$$

• $$\left(3,-3\right)$$

Multiple Choice

How many solutions does the parabola have?

Write the answer on GRAPH 5 of your notes.

• 1

• 2

• 3

• none

Multiple Choice

What is the DOMAIN of the graph?

Write the answer on GRAPH 5 of your notes.

• All real numbers

• $$-1\le x\le11$$

POP QUIZ

​All by yourself.

Answer the last graph on your own.
Turn in when done.