Solving Quadratic Equations
Solve:
4a^2=36
a=\pm 3
Write a quadratic equation in terms of x with the given zeros;
0 \text{ and } \frac{2}{3}
y=x(x-\frac{2}{3})
A company finds that if it charges p dollars for a certain product, it'll sell 1800-4p of them each year.
At what price should the company charge to maximize their revenue?
$225
Solve:
\frac{5}{4}q^2=-\frac{5}{4}
\emptyset
Consider f(x)=-(x+3)^3(x-2)^2 . What's the degree of that function? Also, what are the zeros?
a) Degree is 5
b) Zeros are -3 and 2
A toy store owner estimates that by charging x-dolalrs each for a certain toy, he can sell 40-x toys each week. The quadratic equation R=-x^2+40x is used to find the revenue, R, received when the selling price of a toy is x. Find the selling price that will give him the maximum revenue and then find the maximum revenue.
The selling price is $20 and the maximum revenue is $400
Solve:
(9d-1)(d+4)=0
d=\frac{1}{9},-4
Consider f(x)=-(x+3)^3(x-2)^2 . Describe what happens to the graph of f at each x-intercept.
Crosses the x-axis at
x=-3
Bounces off the x-axis at
x=2
Find the maximum or minimum value of the following equation:
y=3x^2+8x-28
Minimum value at
-\frac{100}{3}
Solve
a^2-a-20=0
a=5,-4
For the function graphed on the board, describe the sign of a, h, \text{ and } k . Are the positive, negative, or zero?
a is positive.
h is positive.
k is negative.
A Veterinarian is enclosing a rectangular outdoor running area against his building for the dogs he cares for. He needs to maximize the area using 100 feet of fencing. The quadratic equation A=x(100-2x) gives the area, A, of the dog run for the length, x of the building that will border the dog run. Find the length of the building that should border the dog run to give the maximum area and then find the maximum area.
The length is 25 feet and the area is 1250 square feet.
Solve
10y^2+57y=-35
y=-\frac{7}{10},-5
A ball that is thrown into the air at time t=0 from an upper floor of a tall building, has some height, in feet, above the ground t-seconds later, given by h(t)=-16t^2+32t+128 . When does the ball hit the ground?
After 4 seconds
Solve the following equation
9x^2-26x-3=0
x=-\frac{1}{9}, 3
Solve
3(x-2)^2=27
x=5,-1
A company finds that if it charges p dollars for a certain product, it'll sell 1800-4p of them each year.
At what price will the company price themselves out of the market? In other words, have no sales at all?
$450
Solve
\frac{1}{2}n^2+\frac{2}{3}n=-1
n=\emptyset
Solve
x^4-9x^2=-20
x=\pm \sqrt{5}, \pm 2
How many and what type of solutions are there in this quadratic equation?
-4x^2+5x+3=0
Two Distinct Irrational Solutions
Find the Domain for the following function:
f(x)=\sqrt{-7x+14}
(-\infty,2]