Solve the following using substitution:
3y-2x=11
y+2x=9
Quadratic Application Tips:
You are almost always solving for
one of two things:
Calculator Tips:
1) To find roots:
1)
2) To find vertex:
3) To find a certain value
a)
2)
b)
Type #1:
1) Two numbers have a sum of 10. Find the largest possible value of their
product.
2) Jim began to create a garden in his backyard. He has 60 feet of fence to
enclose the rectangular garden and he wants to maximize the area. Find the
dimensions for the length and width of the garden that he should use.
3) Suppose that the perimeter of a rectangle is 600 ft. If x represents the width,
then express the area as a function of x. Find the width that would yield the
maximum area.
Type #2:
1) The product of two consecutive odd integers is equal to 30 more than the
first. Find the integers.
2)
The length of a rectangle is three more than twice the width. Determine the
dimensions that will give a total area of 27 m2.
3)
James had a rectangular piece of cardboard that was four times as long as
it was wide. He wanted to use the cardboard to make a box with no lid. To do
this, he first cut a 3-by-3-inch square out of each of the four corners of the
piece of cardboard, as shown in the picture below.
Then James folded the cardboard along the four dotted lines shown in the
picture. This created an open box with a volume of 336 cubic inches. What
was the width of the sheet of cardboard that James started with?
I.
Homework- Show work on a separate piece of paper when necessary.
Solving Quadratics
A. Solve by Factoring
B. Solve by Quadratic Formula
2
2
1. 8r + 3r + 2 = 7r
1. t2-6t=-13
2. 28n2= −96 − 184n
2. m2+12m+36=0
C. Solve by CTS
1. z2-2z-24
D. Other
1. Solve t2-6t+5=0 using all four
methods (Sketch for graphing)
2. t2-3t=7
II.
Quadratic Applications
1. The sum of the squares of two consecutive even integers is 452. Find the
integers.
2. A football is punted into the air. Its height h, in metres, after t seconds is
given by the equation ℎ = −4.9𝑡 ! + 24.5𝑡 + 1
a) How high is the ball after 1 second?
b) Find the maximum height of the ball to one decimal place.
c) When does the ball reach its maximum height?
3. There are 2 positive numbers whose sum is 40. What is the maximum
product of these 2 numbers?
4. A rectangular corral is to be built by stringing an electric fence with y feet
parallel to the side of a river and x feet for each of the 2 sides perpendicular
to the river. The 4th side will be the river. The total length of the fence is to
be 900 feet.
a) Draw a diagram that represents the problem. Label the appropriate parts of
the diagram.
b) Write an equation expressing y in terms of x
c) Let A(x) be the number of square feet area taken up by the corral. Write the
equation A(x). What kind of function is it?
d) Find A(100) and A(300)
e) What is the value of x which makes A(x) maximum? What would be the
maximum area using that value?
f) What values of x make A(x) equal zero?