Key Features of Quadratic Functions Explored

This video tutorial covers key features of quadratic functions, focusing on modeling and graphing. It begins with learning targets, followed by a word problem involving calendar sales. The teacher guides students through deriving expressions for price increases and modeling sales. A function for money raised is created, and students learn to graph it, identifying key points like intercepts and the vertex. The tutorial concludes with analyzing graph behavior and determining maximum profit.

What is the initial price per calendar before any price adjustment?

• $2.50

• $4

• $3.50

• $3

Tags

CCSS.8.EE.C.7B

If the price increases by $0.40, how many calendars are expected to be sold?

• 120

• 150

• 140

• 130

Tags

CCSS.8.EE.C.8C

What is the expression for the number of calendars sold as a function of the price increase x?

• 200 - 30x

• 100 - 10x

• 150 + 25x

• 150 - 25x

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

What is the standard form of the function for the revenue generated from calendar sales?

• -25x^2 + 75x + 450

• 25x^2 + 75x + 450

• -25x^2 - 75x + 450

• -30x^2 + 70x + 400

What is the y-intercept of the revenue graph?

• 500

• 550

• 450

• 400

Tags

CCSS.HSF-IF.C.7A

At what x value does the revenue start to decrease?

• 1.5

• 0.5

• 1.0

• 2.0

What is the maximum revenue that can be achieved?

• $600

• $506.25

• $450

• $500

What price increase leads to the maximum revenue?

• $0.50

• $2.00

• $1.00

• $1.50

What is the vertex of the revenue function?

• (1.5, 506.25)

• (0.5, 475)

• (1.0, 500)

• (2.0, 450)

What does the vertex of the graph represent in this context?

• Break-even point

• Starting price point

• Maximum revenue point

• Minimum revenue point

Tags

CCSS.HSF-IF.C.7A