# Quadratic Equations and Maximum and Minimum Values

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.

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#### Solution Summary

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.

Find the vertex, line of symmetry, and the maximum or minimum value of a quadratic function

Please see the attached file - Don't mind the graphing portion, work what can be worked. I have to input answers not write out the whole equation.

7. Find the vertex, line of symmetry, and the maximum or minimum value of a quadratic function, and graph the function.f(x) = -x +6x +2

The vertex is

8. Find the vertex,line of symmetry, and the maximum or minimum value of a quadratic function, and graph the function.f(x) = -2x +2x +1 . The x-coordinate of the vertex is

9. Find the x-intercepts and y-intercepts f(x) =-x +2x +24

The x-coordinate of the intercepts are x =

10. The carpenter is building a rectangular with a fixed perimeter of 320 ft. What are the dimensions would yield the maximum area ? What is the maximum area?

The length that would yield the maximum area is _________ft

11. Aki's bicycle has determined that when x hundred are built, the average cost per bicycle is given by c(x) = (0.4)x +1.8x +8.926, where c(x) is an hundreds of dollars.

How many bicycles should the shop build to minimize the average cost per bicycle?

12. Find the vertex,line of symmetry, and the maximum or minimum value of a quadratic function, and graph the function f(x) =3x -18x+11. What is the vertex?

13. Find the vertex,line of symmetry, and the maximum or minimum value of a quadratic function, and graph the function f(x)= 10-x . What is the vertex?

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