Exponentials
45 *46
411
Simplify:
4x3-2x2+3+7x3+x2-4x
11x3-x2-4x+3
(2x-3)2
4x2-12x+6
y=-2x2+8x-2
(2,6)
Sketch what does exponential growth look like?
Curves up
215
3x3- 2x + 4 - (2x3+ 3x - 2)
x3 - 5x + 6
Solve:
y=x2-10x-24
x=12, x=-2
y=3(x-4)2+5
(4,5)
How do you find the solution to a system of equations?
where the lines intersect
Is this an example of growth or decay?
y=1/2 (3)x
Growth
2x2(3x3-4x-1)
6x5-8x3-2x2
Solve:
y=6x2-17x+12
x=3/2, x=4/3
What are the transformations?
y=-2(x-3)2+4
flipped, stretch of 2, right 3, up 4
Where do you look to find the solution to a system of inequalities?
shaded region (on a solid line)
You have deposited $100 into the bank and you are making 4% interest. Write an equation to represent this growth.
y=100(1.03)x
(x-4)(x+5)
x2+x-20
Factor by grouping:
2x3+4x2+3x+6
(2x2+3)(x+2)
Sketch the graph of the following equation:
y=-(x+1)2-4
Opens down, left 1, down 4
What causes a quadratic function to have no real solutions?
negative in the square root
The tadpoles are hatching fast. Initially there were 70 tadpoles but this number doubles every month. How many are there in 8 months?
17290
Factor:
x2-8x-20
(x-10)(x+2)
Factor:
7x2+49x
7x(x+7)
What is the shape of a quadratic graph and what is it called?
U-shaped parabola
Solve:
4x+7=-2x+19
x=2