Key Features

Key Features of ALL Functions

TEKS

TEKS A.3C: graph linear functions on the coordinate plane and identify key features, including x‐intercept, y‐intercept, zeros, and slope, in mathematical and real‐world problems

TEKS A.7A: graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x‐intercept, y‐intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry

TEKS A.9C: write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real‐world situations, including growth and decay

​Linear

X-intercepts
Y-Intercepts
Slope
Graphing

Where it crosses the y-axis

Also known as INTIAL AMOUNT or STARTING VALUE

X=0

Y-intercepts

Where it crosses the x-axis

Also known as a ROOTS, ZERO, or SOLUTION

Y=0

​X-intercepts

Intercepts

Multiple Choice

THINK-PAIR-SHARE

What is the x-intercept shown on the graph?

• (2, 0)
• (-2, 0)
• (0, 3)
• (3, 0)

Multiple Choice

THINK-PAIR-SHARE

What is the y-intercept shown on the graph?

• (0, -2)
• (3, 0)
• (0, 3)
• None of these.

Slope

With your partner
Find the slope of the graph.
Write it on your WHITEBOARD when the timer goes off.

​

​TABLE TALK
WHITEBOARD

Multiple Choice

THINK-PAIR-SHARE

Find the slope:

• 3/4
• 4/3
• -3/4
• -4/3

Graphing

​You only need 2 points! Let the computer do the rest.

Today we will focus on using our shortcuts for STANDARD form to find the x-intercept and y-intercept.

Y-intercept

X-intercept

Ax+By=C

Y-intercept

X-intercept

2x+3y=12

Graphing

Now lets use the x-intercept and y-intercept to graph

2x+3y=12

Graphing

TABLE TALK

With your partner

Use the shortcuts for the x & y intercepts.

Then graph the line.

2x+5y=10

​Quadratic

X-intercepts
Y-Intercepts
Vertex
Axis of symmetry
Maximum/Minimum
Graphing

Where it crosses the y-axis

Also known as INTIAL AMOUNT or STARTING VALUE

X=0

Y-intercepts

Where it crosses the x-axis

Also known as a ROOTS, ZERO, or SOLUTION

Y=0

​X-intercepts

Intercepts

What are the zeros of the quadratic functions shown?

Work with your partner.
Write the answer down on the whiteboard when the timer goes off.

​

​THINK-PAIR-SHARE
WHITEBOARD

In Standard form, your a value will be POSITIVE.

Your graph will look like a HAPPY FACE.

Minimum

In Standard form, your a value will be NEGATIVE.

Your graph will look like a SAD FACE.

Maximum

Vertex: the top most or bottom most point

Multiple Choice

THINK-PAIR-SHARE

Does this graph have a minimum or maximum? What point?

• minimum at (-3, -5)

• minimum at (3, 5)

• maximum at (-3, -5)

• maximum at (3, 5)

Axis of Symmetry

Multiple Choice

THINK-PAIR-SHARE

What is the green dashed line called?

• roots or x-intercepts
• parabola
• axis of symmetry
• line of dashes

Multiple Choice

THINK-PAIR-SHARE

A parabola has a vertex at (-3,2).
Where is the axis of symmetry?

• y = -2
• x = 3
• x = -3
• y = 2

Multiple Choice

THINK-PAIR-SHARE

What is the equation for axis of symmetry?

• y=3
• x=3
• x=5
• x=1

Writing Exponential Functions

a is your INTIAL VALUE or STARTING AMOUNT.

b is your GROWTH or DECAY rate
Growth will be MORE than 1
Decay will be LESS than 1 but MORE than 0.

x is ALWAYS your exponent

​Identify the a and b value.
Write the equation.

Researchers studied the population of a town over time and modeled the data using an exponential function.

• The initial estimated population was 48,000.

• After the first year, the population of the town was 50,400.

​INK-PAIR-SHARE & WHITEBOARD
Identify the a and b value.
Write the equation.

A sample of a substance with an initial mass of 963 grams is decaying at a rate of 27% per hour.

Multiple Choice

THINK-PAIR-SHARE

Write an exponential function to model the situation. You invest $1500. Your investment increases at a rate of 3.5%.

• f(x) = 1500(0.965)^x

• f(x) = 1500(1.035)^x

• f(x) = 1500(.035)^x

• f(x) = 1500(1.965)^x