Quadratic Functions and Equations Overview
2/29 Warm Up-
Monday
Test Today!
Make sure you have:
•
BACKPACKS IN BACK OF ROOM
•
Something to write with
•
Flipchart
•
Calculator
2/29 Test Tips
3/1 Warm Up-
Tuesday
Finishing Test Today!
Make sure you have:
•
BACKPACKS IN BACK OF ROOM
•
Something to write with
•
Flipchart
•
Calculator
3/1 Test Tips
3/2 Warm Up-
Wednesday
Solve the formula pV = nRT for n.
A. n = pV – RT
B. n = pVRT
C. n =
pV
RT
D. n = pV
Show your work OR explain your
reasoning here.
3/2 Objective:
I will be able to graph
quadratic functions in
standard form.
Quadratics
ax
2
+ bx + c =0
Standard Form of Equation
the
u-shaped curve
a
quadratic equation makes
when graphed.
Parabola
Types of Parabolas
If ‘a’ is
POSITIVE
, the parabola
will
OPEN UPWARD
If ‘a’ is
NEGATIVE
, the
parabola will
OPEN
DOWNWARD
Axis of Symmetry
•
The vertical line that
divides
the parabola into two equal
parts.
•
It is
the x-value of quadratic
equation
.
•
To find
x-value use this
formula:
Vertex
•
The
turning point of the parabola
.
•
Written as
(x, y)
•
To find vertex:
•
use axis of symmetry formula
to
find x.
•
plug x
into equation to find y.
Types of Vertex
•
Minimum
:
•
vertex is lowest point
•
‘a’ is positive
•
Maximum:
•
vertex is highest point
•
‘a’ is negative
3/3 Warm Up-
Thursday
A plumber finished three jobs on Tuesday.
The first two only cost the owner the $45
trip fee because they took very little time
to complete.
For the third job, the plumber charged
the trip fee plus 6 times his hourly rate.
If the plumber received a total of $303 for
the day, what is the hourly rate?
I will be able to graph quadratic
functions in standard form.
3/3 Objective
3/3 Example:
Axis of Symmetry
Vertex (plug in x- value)
y = ( )
2
– 4( )+ 5
y = x
2
– 4x + 5
Maximum or Minimum?
Graph:
3/3 Example:
Axis of Symmetry
Vertex (plug in x- value)
y = -( )
2
+ 2( ) - 1
y = -x
2
+ 2x - 1
Maximum or Minimum?
Graph:
Graphing Quadratic Equations
Worksheet
3/3 Assignment
3/4: Warm Up-
Friday
An architect builds a scale model of a
skyscraper for a land development
proposal.
•
The model is 2 ft tall.
•
The scale of the model is
1 in. : 12.3 m.
•
How tall is the proposed
skyscraper in meters?
Show your work.
3/4 Objectives
I will be able to graph
quadratic functions in
standard form.
3/4 Example: Calculator
y = x
2
– 4x + 5
•
Plug equation into y=
•
Go to 2
nd
Graph
•
Vertex: where is the turning point?
•
Axis of Symmetry: what is the x-value of the
turning point
•
Graph: choose 2 points higher than vertex and
2 points lower and graph.
•
Maximum or Minimum?
3/4 Example: Calculator
•
Plug equation into y=
•
Go to 2
nd
Graph
•
Vertex: where is the turning point?
•
Axis of Symmetry: what is the x-value of the
turning point
•
Graph: choose 2 points higher than vertex and
2 points lower and graph.
•
Maximum or Minimum?
y = -x
2
+ 2x - 1
Explore the essentials of quadratic functions and equations, covering topics such as standard form, parabolas, types of parabolas, and axis of symmetry. Understand how to graph quadratic functions in standard form and key tips for solving quadratic equations. Get ready with your backpack, writing tools, and calculator for the upcoming tests.
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Presentation Transcript
2/29 Warm Up 2/29 Warm Up- - Monday Test Today! Test Today! Make sure you have: BACKPACKS IN BACK OF ROOM Something to write with Flipchart Calculator
2/29 Test Tips 2/29 Test Tips What to do? multiply a times c ax2 + bx + c + + ax2 bx + c factor using y= number/x second graph write whole numbers on t chart add them to make b ax2 + bx c + + ax2 bx c divide by a reduce fraction using alpha y= enter move bottom number to front
3/1 Warm Up 3/1 Warm Up- - Tuesday Finishing Test Today! Finishing Test Today! Make sure you have: BACKPACKS IN BACK OF ROOM Something to write with Flipchart Calculator
3/1 Test Tips 3/1 Test Tips What to do? multiply a times c ax2 + bx + c + + ax2 bx + c factor using y= number/x second graph write whole numbers on t chart add them to make b ax2 + bx c + + ax2 bx c divide by a reduce fraction using alpha y= enter move bottom number to front
3/2 Warm Up 3/2 Warm Up- - Wednesday Solve the formula pV = nRT for n. Show your work OR explain your reasoning here. A. n = pV RT B. n = pVRT C. n = pV RT D. n = pV
3/2 Objective: 3/2 Objective: I will be able to graph quadratic functions in standard form.
ax2 + bx + c =0 Standard Form of Equation
Parabola the u-shaped curve a quadratic equation makes when graphed.
Types of Parabolas If a is POSITIVE, the parabola will OPEN UPWARD If a is NEGATIVE, the parabola will OPEN DOWNWARD
Axis of Symmetry The vertical line that divides the parabola into two equal parts. It is the x-value of quadratic equation. To find x-value use this formula:
Vertex The turning point of the parabola. Written as (x, y) To find vertex: use axis of symmetry formula to find x. plug x into equation to find y.
Types of Vertex Minimum: vertex is lowest point a is positive Maximum: vertex is highest point a is negative
3/3 Warm Up 3/3 Warm Up- - Thursday A plumber finished three jobs on Tuesday. The first two only cost the owner the $45 trip fee because they took very little time to complete. For the third job, the plumber charged the trip fee plus 6 times his hourly rate. If the plumber received a total of $303 for the day, what is the hourly rate?
3/3 Objective 3/3 Objective I will be able to graph quadratic functions in standard form.
3/3 Example 3/3 Example:: y = x2 4x + 5 Maximum or Minimum? Axis of Symmetry Graph: Vertex (plug in x- value) y = ( )2 4( )+ 5
3/3 Example 3/3 Example:: y = -x2 + 2x - 1 Maximum or Minimum? Axis of Symmetry Graph: Vertex (plug in x- value) y = -( )2 + 2( ) - 1
3/3 Assignment 3/3 Assignment Graphing Quadratic Equations Worksheet
3/4: Warm Up 3/4: Warm Up- - Friday An architect builds a scale model of a skyscraper for a land development proposal. The model is 2 ft tall. The scale of the model is 1 in. : 12.3 m. How tall is the proposed skyscraper in meters? Show your work.
3/4 Objectives 3/4 Objectives I will be able to graph quadratic functions in standard form.
3/4 Example: Calculator 3/4 Example: Calculator y = x2 4x + 5 Plug equation into y= Go to 2nd Graph Vertex: where is the turning point? Axis of Symmetry: what is the x-value of the turning point Graph: choose 2 points higher than vertex and 2 points lower and graph. Maximum or Minimum?
3/4 Example: Calculator 3/4 Example: Calculator y = -x2 + 2x - 1 Plug equation into y= Go to 2nd Graph Vertex: where is the turning point? Axis of Symmetry: what is the x-value of the turning point Graph: choose 2 points higher than vertex and 2 points lower and graph. Maximum or Minimum?
