Exoponentials
What are the zero term and the multiplier?
y = 12(0.34)x
Zero term: 12
Multiplier: 0.34
What strategy would be used to solve this system of equations?
x = 3y - 2
2x - 3y = 5
Substitution
Factor:
x2 + 10x + 9
(x+1)(x+9)
What are two other words for 'x-intercept'?
Root
Zero
What is the y intercept of this quadratic?
y = x2 - 5x + 6
y-int:(0,6)
Give an example of an equation that shows an exponential decay of 30%.
y = a(0.7)x
What strategy would be used to solve this system of equations?
2x - 3y = 5
4x + y = 3
Elimination
Factor:
x2 - 5x + 6
(x-2)(x-3)
Solve for the roots:
x2 - 5x + 6 = 0
x = 2
x = 3
What are the x-intercepts of this graph?
y = x2 - x - 6
(3,0)
(-2,0)
Give an example of an equation that shows an exponential growth of 25%.
y= a(1.25)x
Solve using Substitution:
x = 3y - 2
2x - 3y = 5
(7,3)
Factor:
x2 - x - 20
(x+4)(x-5)
Solve for the roots:
x2 - 7x - 8 = 0
x = -1
x = 8
A parabola has roots of x = 2 and x = -4
What is its line of symmetry?
x=-1
Marco doubles his stamp collection every year. Next year he will have 100. Write an equation for his situation.
y = 50(2)x
Solve the system of equations:
6x + 4y = -1
6x + 5y = 2
( -13/6, 3 )
Factor:
4x2 - 9
(2x-3)(2x+3)
Solve for the roots:
x2 - 25 = 0
x = 5
x = -5
A parabola has roots of x = -2 and x = 2
Its equation is y = x2 - 4
What point represents the vertex?
(0,-4)
Helium decays in water at a rate of 15% every minute.
One minute from now, there are 17 ml in a cup of water.
Write an equation for this situation and find how long it will take for less than 10ml to be present.
y = 20(0.85)x
after 4 min
Solve the system of equations:
-4x + y = 6
-3x + 6y = - 6
(-1,2)
Factor:
6x2 + -11x + 3
(2x-3)(3x-1)
Solve for the roots:
3x2 + 11x + - 4 = 0
x = -4
x = 1/3 or (.333)
Graph the following on the back of your whiteboard.
y = x2 - 2x - 3
Make sure you have the:
Roots
y-intercept
line of symmetry
vertex
FIVE total graphed points
Roots: (-1,0) (3,0)
Y-intercept: -3
Line of Symmetry: x = 1
Vertex: (1, -4)