Quadratic Functions

Standard Form, Vertex Form, and Factored Form

100

Does this graph open up or down?

y=-3x²-6x-4

Down (Negative Nancy)

200

 What is the vertex of y=-2x²-4x-5

(-1,-3)

300

What is the y- intercept

y=-3x²-5x-4

-4 or (0,-4)

400

What is the axis of symmetry?

f(x)=7(x-4)(x+5)

x= (4+-5)/2

x= -1/2

500

What is the vertex? AND how many zeros will this function have?

y=(x+2)²+4

Vertex (-2,4) 

and it is opening up to it has no zeros

Converting Forms

100

Convert to vertex form(hint complete the square):

g(x)=x²-6x+14

g(x)=(x-3)²-25

200

What is this in factored form?

h(x)=x²-16x+60

h(x)= (x-10)(x-6)

300

f(x)=x²-6x+27

What are the x- intercepts?

9 and -3

(9,0) (-3,0)

400

Convert to Standard Form

f(x)= 3(x-1)(x+2)

f(x)= 3x²+3x-6

500

What is the minimum value of the function?

(Hint: find the y value of the vertex)

f(x)= x²+10x+29

4

Transformations

100

What transformation occurred:

f(x)= x²-1

f(x)= (x-1)²-1

Right 1

200

Translate f(x) up 3. What is the new function?

Start with f(x) = 3x²+5

3x²+8

300

Let f(x)= 1/2x²+4

The function g(x) is a vertical stretch of f(x) by a factor of 4

What is g(x)

g(x)= 2x²+16

400

If f(x)= x²

Write a function for g(x) that is reflected over the x axis

g(x)= -x²

500

If f(x) = x²

and g(x)= (x+2)²-5

Describe the transformation

Left 2, Down 5

Rates of Change

100

f(x)= x²-2x-4

What is the average rate of change from x=-1 to x=4

1

200

What is the average rate of change for f(x)=x²+3x-4 from x=-3 to x=8

8

300

Let f(x)= -0.5(x-8)²-2

Find the average rate of change from x=-4 to x=8

6

400

Which one goes at the faster rate as x increases:

A) y= (2)(3^x)

B) y=10x+15

C) y= 5x²+x+10

A

500

How do you find the average rate of change?

f(b)-f(a)/ b-a

Linear and Quadratic Systems

100

Using your Graphing Calculator (Desmos), what are the ordered pairs of the solutions. (Where do the graphs meet?)

y=2x+1

y=2x²+1

.

(0,1) (1,3)

200

How many solutions does the system have?

y=−3x+5

y=x²−3x+5

1

300

What are the solutions of the system?

 y=−6x−6

y=x²−5x−6

(-1,0) (0,-6)

400

This system has one solution.

y=5x−9

y=x²−3x+7

What is the y-coordinate of the solution?

11

500

Skylar repairs microwaves. Her revenue, in dollars, can be modeled by the equation y = 80 + 30x, where x is the number of hours spent repairing microwaves. Her overhead cost, in dollars, can be modeled by the equation  y=10x²−20

 , where x is the number of hours spent repairing microwaves.

After how many hours does she break even?

Note: The phrase break even refers to the value where the two functions are equivalent.

5