SUMMARY Algebra OneQuadratics in Standard Form - using different methods for analyzing.

Use this worksheet to help you prepare for a quiz next class! This will be collected with all work. Answers are posted on my calendar for checking, but the work should be your own!

Questions to ask yourself…

1) Is the function in standard form?

  1. If yes – try to factor and then use intercept form techniques to find x-intercepts and AOS and vertex.
  2. If no – put in standard form and try to factor (see (a) above)

2)Can you factor the function equation?

  1. If yes then do it and then use intercept form techniques to find x-intercepts and AOS and vertex.
  2. If no go to step 3 below..

3)If you can’t factor – Does b = 0?

  1. If yes b = 0 then use square root method to find x-intercepts and –b/(2a) to find AOS (& x-value of vertex) which you plug into original function to find y-value of vertex.
  2. If no then use quadratic formula to find x-intercepts and –b/(2a) to find AOS (& x-value of vertex) which you plug into original function to find y-value of vertex.

Analyze the following functions COMPLETELY,do not use the graphing function of your calculator, algebraic work must be shown as appropriate.

a)Identify whether the function opens up or down (using the leading coefficient, not the graphing function of your calculator)

b)Find the x-intercepts

c)Find the AOS

d)Find the vertex (ordered pair) and state whether it is a maximum or minimum

e)Find the y-intercept

f)Draw a graph

g)Find the point symmetric to the y-intercept

h)Describe the domain & range using interval notation

Use separate paper to do the analysis – I recommend one problem per side of paper so you have plenty of room for work. Answer key will be posted on my calendar.

1) y = x2 – 5x – 24

2)y = -5x2 + 80

3)y = 6x2 + 13x – 5

4)y = ½ x2 – 20

5)y = - ¼ x2 – 3x – 8

6)y = x2 – 10x + 22

7)y = x2 – 6x + 3

8)y = 2x2 + 5x + 11

when the x-intercepts are imaginary – they do not cross the x axis but you should still state them as they are still “zeros” of the function.

AREA PROBLEMS

9)A local grocery store has plans to construct a rectangular parking lot on land that is bordered on onesideby a highway. There are 1280 feet of fencing available to enclose the other three sides. [Letxrepresent thelengthof the two parallel sides of fencing.] Find the dimensions that will maximize theareaof the parking lot. Also state the maximum area.

10) CHALLENGE (bonus type) A rancher has 1200 feet of fencing to enclose two adjacent rectangular corrals of equal lengths and widths as shown in the figure below. What is the maximumareathat can be enclosed in the fencing? What dimensions will result in this area. This one is a challenge!

DROPPED OBJECT PROBLEMS – Remember the formula h = -16t2 + s for solving these! (s = starting height, h = ending height with both in feet)

11) Twenty seconds after launching, a foam tile fell off the space shuttle. This occurred at 45,000 feet. How long after lift-off did the tile hit the ground?

12) Professional cliff divers perform their dives down from a platform at a maximum height of 28 meters. A slight error in timing may lead to danger for their lives. At diving the impact is nine times harder compared to a dive from a starting height of 10 meters. The “entering speed” into the water can get as high as 100 km/hour! Besides courage, extraordinary physical control is needed to do this intense sport.

How long does it take a cliff diver to reach the water once she has jumped from the height of 28 meters? (conversion information: 28 meters ≈ 92 feet)