Lesson 4.07 Characteristics of Quadratic Functions

Match

Warm-Up

Match the following

-5

-1

-4

undefined

• -5

• -1

• $$\frac{2}{5}$$

• -4

• undefined

Lesson 4.07- Characteristics of Quadratic Functions

Standard: A.FGR.7.3

Learning Target(s)

• I can identify the key characteristics of a quadratic function including domain, range, and x-intercept(s).

• I can find the average rate of change (AROC) of a quadratic function.

Multiple Choice

What is the domain of the graph?

• All real numbers

• To infinity and beyond

• y ≥ 0

• x ≥ 0

Multiple Choice

What is the domain of the parabola created by the ball?

• Domain : 0 ≤ d ≤ 280

• Domain : 0 ≤ h ≤ 150

• Domain : 0 ≤ d ≤ 570

• Domain : 0 ≤ h ≤ 280

Multiple Choice

What is the range for the function below? 

• y ≤ 4
• y ≥ 4
• All real numbers
• -3 ≤ y ≤ 1

Multiple Choice

What is the range of the graph?

• All real numbers
• To infinity and beyond
• y ≥ 0
• x ≥ 0

Zero of Quadratic Functions

• A value k whereas f(k)=0. (The X - values of the x-intercepts.)

Multiple Choice

Use the graph to determine the solutions.
*Hint: Solutions = roots = zeros = x-intercepts

• -1 and -3
• 1 and -3
• 1 and 3
• -1 and 3

Multiple Choice

The x-intercepts of a quadratic equation are known as the _____.

• vertices

• squares

• zeros

• formulas

Multiple Select

What is another name for the x-intercepts of a quadratic?

• Roots

• Zeros

• x-axis

• Solutions

Multiple Choice

What do we call the highest or lowest point of a quadratic?

• parabola

• vertex

• graph

• point

Multiple Choice

What is the vertex?

• (2, 4)

• (3, -1)

• (0, 8)

• (4, 2)

Multiple Choice

What is the minimum value of the quadratic function?

• -3

• -1

• All real numbers

• 1

Multiple Choice

Determine if the function graphed has a maximum or a minimum value and identify that value.

• maximum at -1

• minimum at -1

• maximum at 4

• minimum at 4

Multiple Choice

What is the arrow pointing at? How can you use this value to determine the minimum/maximum values?

• The arrow is pointing at the y-intercept. The y value of this point is equivalent to the maximum/minimum

• The arrow is pointing at the vertex. The x value of this point is equivalent to the maximum/minimum

• The arrow is pointing at the solution. The y value of this point is equivalent to the maximum and the x value is equivalent to the minimum

• The arrow is pointing at the vertex. The y value is equivalent to the minimum/maximum

Multiple Choice

As x increases, f(x)...

• Increases

• Decreases

• Stays the Same

• Goes to the vertex

Multiple Choice

As x decreases, f(x)...

• Increases

• Decreases

• Stays the Same

• Goes to the vertex

Average Rate of Change

Average Rate of Change- Change in output (y) divided by the change in input (x)

Average Rate of Change is the slope between any two points of a function.

How to find the Average Rate of Change:

Multiple Choice

Use the given function or the graph to find the average rate of change

• 5

• -1/5

• -5

• 15

Multiple Choice

Use the given function or the graph to find the average rate of change

• 3

• -3

• 3/2

• -1/3

Multiple Choice

Given the function $$f\left(x\right)=x^2+3x-1$$ , determine the average rate of change of the function over the interval $$-3\le x\le4$$ .

• $$\frac{4--3}{27--1}=\frac{7}{28}=\frac{1}{4}$$

• $$\frac{-1-27}{4--3}=\frac{-28}{7}=-4$$

• $$\frac{27--1}{4--3}=\frac{28}{7}=4$$

Multiple Choice

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

• 2
• 1/2
• -2
• -1/2

Open Ended

What do $$\frac{\Delta y}{\Delta x}$$ , $$\frac{change\ of\ output\ values}{change\ of\ input\ values}$$ , $$\frac{y_2-y_1}{x_2-x_1}$$ and $$\frac{f\left(b\right)-f\left(a\right)}{b-a}$$ all have in common?

Poll

How do you feel about characteristics of quadratic functions?

• I'm clueless

• I need more practice

• I got this!

IXL - Domain and range of quadratic functions: graphs (Algebra 1 practice)

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IXL - Checkpoint: Average rate of change (Algebra 1 practice)

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