Lesson 1-4

Intro to Quadratics

100

What does Area measure?

The amount of space an object takes up OR the space inside an object 

200

FILL-IN-THE-BLANK 

Area is maximized (at its maximum) when the _______-__________ are equal

side - lengths

300

What is the general shape of a quadratic graph?

A hill , rainbow, arch, 

** any other shape that is similar to one of those **

400

FILL-IN-THE-BLANK 

On a quadratic graph, there will be two

 __ -values for every ___-value, except at the vertex

1st blank - Y

2nd blank  - X

500

What is the general form of the Quadratic Equation ? 

ax2 + bx + c

Patterns

100

How can you determine that a pattern is growing linearly?

It has a common difference / the same number is being added or subtracted.

200

How can you determine that a pattern is growing exponentially?

It has a common factor / the same number is being multiplied or divided

300

How can you determine that a pattern is growing quadratically?

What is 2²

400

How is this pattern growing? 

{ 2 , 5 , 10 , 17 , 26 }

Quadratically - the difference between the numbers increased by 2 for each input :  +3, +5, +7, +9

500

How is this pattern growing? 

{ 2 , 6 , 18 , 54 , 162 }

Exponentially - there is a common factor of 3

Writing Equations

100

If a row and column are added as the step number increases by 1, then the function is _____________

Quadratic

200

Are these two functions equivalent? How ?

n(n-4) & n² - 4n

Yes , the second equation is the first one with the n value distributed

300

Write an equation to represent the following data : 

{ 0 , 1 , 4 , 9 , 16 , 25 }

Y = n²

400

Write an equation to represent the following data : 

{ 3 , 6 , 12 , 24 , 48 , 96 }

Y = 3•2ⁿ

500

Write an equation to represent the following data : 

{ -1 , 0 , 3 , 8 , 15}

Y = n² -1

Exponential vs. Quadratic

100

True or false : 

A quadratic function will always grow faster than an exponential function

False

200

Given an equation y = 4x² and an x-value of 2, what are the steps to solving for y? (PEMDAS)

Substitute 2 for x and square it to get 4, then multiply 4 x 4 to get y = 16

300

Which function grows faster between 0 and 4?

f(x) = 6x² OR P(x) = 3^x

f(x) = 6x²

400

Which function grows faster over time? Why? 

f(x) = 12x² OR p(x) = 2^x

p(x) = 2^x because it represents an exponential function

500

Why do exponential functions eventually grow faster than quadratic functions?

Because exponential functions involve more numbers multiplied together whereas quadratic equations only have 2 numbers

 (x² vs. 2^x)

RANDOM

100

What is Mr. Gutierrez's first name?

What is Orion

200

Does Mr. Gutierrez have siblings?

What is yes

300

How many cats do Mr.Gutierrez have?

What is 3

400

What college did Mr.Gutierrez graduate from?

What is CSULB

500

What is Mr.Gutierrez's ethnicity?

What is Mexican