2/5 one day Classwork assignment

Lesson Presentation

Warm-Up: Vaulting Moves

Vaulting is an exercise in which gymnasts leap over an
apparatus and perform a skill in mid-air. The image
shows a frame-by-frame pictorial of a gymnast’s vault
routine. Based on the compilation of moves performed
by the gymnast, a sketch of a parabola was drawn.

Math Nation - Unit 9, Lesson 2 - Writing a Quadratic Function From a Graphic - Volume 2, PAGE 65

1.Explain whether the 𝑎 value of the
parabola is positive or negative.

2.If each square is 1 by 1, what are the
vertex and 𝑥-intercepts of the parabola?

vertex

𝑥-intercepts

Fill in the Blanks

What is my vertex?

Fill in the Blanks

What are my x-intercepts?

Guided Instruction: Writing a Quadratic Function in Vertex Form from a Graph

Hudson is starting a lawn-mowing business in his
neighborhood. He creates a graph to help him determine
what to charge customers per mow to maximize his profits.
He uses 𝑥 to represent the cost of each lawn he mows and
𝑦 to represent the profit in dollars ($).

1.The point represents the maximum

profit Hudson can make. This point on a graph is

called the __________ of the parabola.

2.Discuss with your partner what you notice about
points (20, 190) and (40, 190).

Math Nation - Unit 9, Lesson 2 - Writing a Quadratic Function From a Graphic - Volume 2, PAGE 66

Fill in the Blanks

The point is

represents the maximum profit

Fill in the Blanks

It is called the

The steps in the table show how to use the point (20, 190) and the vertex (30, 240) to find the
quadratic function in vertex form 𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘, where (ℎ, 𝑘) is the vertex.

The quadratic equation Hudson graphed is 𝑦 = − (𝑥−30)2 + 240.

Math Nation - Unit 9, Lesson 2 - Writing a Quadratic Function From a Graphic - Volume 2, PAGE 67

Collaboration: Writing a Quadratic Function Using a Vertex and Point From a Graph

With your partner, use the other point identified on Hudson’s graph, (40, 190), along with the
same vertex, (30, 240), to generate another quadratic equation in vertex form.

Math Nation - Unit 9, Lesson 2 - Writing a Quadratic Function From a Graphic - Volume 2, PAGE 67

Math Response

Step 3: Solve for a

a =

Type answer here

Correct Answer: -\frac{1}{2}

Deg^°

Rad

Drag and Drop

Step 4: substitute in the vertex and a into our vertex equation;

​

Placeholder

= ​

Placeholder

(x-​

Placeholder

)² + ​

Placeholder

---

Drag these tiles and drop them in the correct blank above

30

240

a.The quadratic equation with vertex (30, 240) and point (40, 190) is

___________________________.

b.Discuss with your partner what you notice about quadratic functions with the same vertex and two points that are equidistant from the vertex. Summarize your discussion.

Math Nation - Unit 9, Lesson 2 - Writing a Quadratic Function From a Graphic - Volume 2, PAGE 67

a.The quadratic equation with vertex (30, 240) and point (40, 190) is

___________________________.

b. Discuss with your partner what you notice about quadratic functions with the same vertex and two points that are equidistant from the vertex. Summarize your discussion.

Math Nation - Unit 9, Lesson 2 - Writing a Quadratic Function From a Graphic - Volume 2, PAGE 67

2.

A quadratic function is graphed with the vertex and two points equidistant from the vertex labeled.

a. Write the equation in vertex form for the quadratic function graphed.

Math Nation - Unit 9, Lesson 2 - Writing a Quadratic Function From a Graphic - Volume 2, PAGE 68

Drag and Drop

Step 1: substitute the values for the vertex (2, 1)

y = a (x-​

Placeholder

)² + ​

Placeholder

Drag these tiles and drop them in the correct blank above

2

1

4

5

8

6

9

16

Drag and Drop

Step 2: substitute the values for for the point (0,21)

Placeholder

= a (​

Placeholder

-​

Placeholder

)² +​

Placeholder

Drag these tiles and drop them in the correct blank above

21

0

2

1

4

11

45

3

Math Response

Solve the a.

a =

Type answer here

Correct Answer: 5

Deg^°

Rad

Drag and Drop

Step 4: substitute a into our vertex formula

y = ​

Placeholder

(x-​​

Placeholder

)² + ​

Placeholder

Drag these tiles and drop them in the correct blank above

5

2

1

b.

The quadratic equation is _____________________.

c.Rewrite the equation into standard form 𝑦 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐.

Math Nation - Unit 9, Lesson 2 - Writing a Quadratic Function From a Graphic - Volume 2, PAGE 68

Drag and Drop

Rewrite the equation in Standard form.

y = ​ ​

Placeholder

-​

Placeholder

+​

Placeholder

Drag these tiles and drop them in the correct blank above

21

41

57

68

Your Turn!

Math Nation - Unit 9, Lesson 2 - Writing a Quadratic Function From a Graphic - Volume 2, PAGE 69

1.

Complete the table for each
quadratic function using the
graph of the function.

Your Turn!

Math Nation - Unit 9, Lesson 2 - Writing a Quadratic Function From a Graphic - Volume 2, PAGE 69

1.

Complete the table for each
quadratic function using the
graph of the function.

Math Nation - Unit 9, Lesson 2 - Writing a Quadratic Function From a Graphic - Volume 2, PAGE 70