Algebra I 4/3

Intercepts

100

Where do x-intercepts occur on a quadratic graph, and what is specific about these points? 

The occurs when a graph crosses the x-axis, what is specific about these points is that their y-value is always zero.

200

Find the x-intercepts of y=(x−3)(x+5).

x=3, -5

(3,0) , (-5,0)

300

Find the y-intercepts of y=x^2−9

y=-9

(0,-9)

400

Find the y-intercept of the equation (19,987,542x+2)(34,521,239x-7)

y= -14

(0,-14)

500

Find the x-intercepts of y=x^2−9. 

x= -3, 3

(-3,0) , (3,0)

Vertex

100

What's the vertex of x^2?

(0,0)

200

What's the vertex of x^2-3?

(0,-3)

300

What is the relationship between a vertex and the x-intercepts of a quadratic?

The x-value of a vertex is halfway between the x-intercepts of the quadratic

400

What's the x-value of the vertex for the equation (x+2)(x-4)

Since the x-intercepts are x=-2 and 4, halfway between these is 1

x=1

500

What is the vertex of (x+1)(x-3)

(1, -4)

Forms

100

Sort the following into vertex, standard, or factored form

1. x^2+2

2. (x-1)^2-1

3. (x+3)(x-1)

1. Standard

2. Vertex

3. Factored

200

Convert the following to standard form: (x+2)(x-5)

x^2-3x-10

300

State which form is most efficiently used when solving for the following:

1. x-intercepts

2. y-intercepts

3. vertex

1. Factored Form

2. Standard Form

3. Vertex Form

400

Convert the following to standard form: (3x-3)(-5x+2)

-15x^2+21x-6

500

Convert to standard form: -(x+2)^2 -1

-x^2-4x-5

Quadraticss

100

T/F: Quadratics increase quicker than exponential equations

False!

200

Quadratics in standard form have the following equation:

                                                   ax^2+bx+c

How does changing c affect the graph of the quadratic?

It shifts the graph up or down depending on if c is positive or negative

300

How does increasing a to 10, 100, 1,000, etc. affect the graph:

a(x+b)^2

The graph becomes much more narrow as you increase a. The y-values increase at a much quicker rate.

400

If you wanted to "flip" a quadratic upside down, how would you accomplish this?

ax^2+bx+c

Make a negative. Note that changing the signs of b and c will change the graph, but it will not "flip" the graph upside down

500

Give a real life example of where we see quadratic in our everyday life

Responses vary; shooting a basketball, kicking a soccer ball, throwing a football, bridges, arches, etc. 

Shifting Quadratic Graphs

100

What equation would shift the graph of x^2 up nine units?

x^2 + 9

200

What equation would shift the graph of x^2 to the right 2 units

(x-2)^2

300

What equation would shift the graph of x^2 down 4 units and left 2 units?

(x+2)^2 - 4

400

What equation would shift the graph of x^2 right 3 units, down 6 units, and flip upside down?

-(x-3)^2 + 6

500

What equation would shift the graph of x^2 right 6 units, down 8 units, flip upside down, and increase at a more rapid rate?

Response vary; as long as a>1, any of the following answers work:

-5(x-6)-8