Q1: Student has difficulty starting

You are given two pieces of information. Which form of a quadratic equation can you match the information to?

Q2: Student uses an inefficient method

What does an equation in standard form tell you about the graph?

What an equation in completed square form tell you about the graph?

Student makes a technical error

Check your answer

Student correctly answers all questions

Can you think of any more coordinates for the key features of the graphs 1,2,3 and 4? Explain your answer.

Another quadratic has the same coordinates for the minimum but the y-intercept is (0,14). What is the equation of this curve?

Turning Points

How many turning points does each of your graphs have? Is it a maximum or a minimum?

Can the curve of a quadratic function have more than one turning point?

Can it have no turning points?

Roots

How many roots does your graph have?

Where are these roots?

How many roots can a quadratic have?

Turning Points: Just 1

Y-intercepts

Do all quadratic curves have a y-intercept?

Can a quadratic have more than one y-intercept?

Turning Points: 1Roots: 0, 1, or 2 Real roots

Domain and RangeDescribe your graph to using the words

up/down/right/left

Did you color the entire x-axis?

Color the x-axis where your graph has an x-value

Color the y-axis where your graph has a y-value?

Did you color the entire y-axis?What is the relationship between the maximum or minimum and the y-

values?

Review

• Turning points: 1 (maximum or minimum)

• Real Roots (x-intercepts) 0, 1, 2

• Y-intercept: Always just 1

• Domain: All Real numbers

• Range: Maximum: y < y value of vertex

• Minimum: y > y value of vertex

Graphs

Standard Form

1. y = x2 – 10x + 24

Factored Form

2. y = (x-4)(x-6)

Completed Square Form

3. y = (x-5)2 - 1

4. y = -(x+4)(x-5) 5. y = -2(x+4)(x-5)

Mathematical Practices Specific Concept Reasoning (Activity)

1. Make sense of problems & persevere in solving them.

2. Reason abstractly & quantitatively.

3. Construct viable arguments & critique reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for & make use of structure.

8. Look for and express regularity of repeated reasoning.