Note that x^y computes any number to any power (integer, fraction, decimal).
1)Using the quadratic equation x2 - 3x + 2 = 0, perform the following tasks:
a)Solve by factoring.
b)Solve by completing the square.
c)Solve by using the quadratic formula.
2)For the function y = x2 - 6x + 8, perform the following tasks:
a)Put the function in the form y = a(x - h)2 + k.
b)What is the line of symmetry?
c)Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x - h) 2 + k.
Show graph here.
Explanation of graphing.
d)In your own words, describe how this graph compares the graph of y = x2?
3)Suppose you throw a baseball straight up at a velocity of 32 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
·16 represents ½g, the gravitational pull due to gravity (measured in feet per second 2).
·is the initial velocity (how hard do you throw the object, measured in feet per second).
s the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.
a)What is the function that describes this problem?
b)The ball will be how high above the ground after 1 second?
c)How long will it take to hit the ground?
d)What is the maximum height of the ball?
4)Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). She wants to maximize the area of her patio (area of a rectangle is length times width). What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation.© BrainMass Inc. brainmass.com August 17, 2018, 10:44 am ad1c9bdddf
Quadratic Equations and Maximum and Minimum Values are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.