Exponential Functions
y = 3(2x) - 4
y-int is -1
f(x) = (x-3)(x+5)
y = -2x + 5
Slope = -2
y-int = 5
Why did the math book look so sad?
Because it had so many problems.
Given the table below:
time in sec 2 5 7
Height in m 34 38 24
Given that the height can be modeled by a quadratic in the form h(t) = at2 + bt + c, where a, b, c are real #'s.
SHOW THAT 4a + 2b + c = 34
h(t) = at2 + bt + c
We know from 4a + 2b + c = 34, that h(t) = 34 and from the table t = 2
a(2)2 + b(2) + c = 34 so 4a + 2b + c = 34
What is the domain and range of the exponential function y = 3(2x) - 4?
D: All Reals
R: y > -4
If the axis of symmetry is x = -1, and the point (-5,4) is a point on the quadratic, name one other point that is also on the quadratic.
(3,4)
Find the slope of the equation that goes through the points (-2, 3) and (4,5)
1/3
Why can't you argue with a 90 degree angle?
Because it's always right.
Use the table to write two more equations in terms of a, b, and c.
(recall the first equation is 4a + 2b + c = 34)
Time (s) 2 5 7
Height (m) 34 38 24
25a + 5b + c = 38
49a + 7b + c = 24
What is the equation of the horizontal asymptote of the exponential function y = -2(0.5x) + 3?
y = 3
Given the equation f(x) = (x-3)2 - 4, what is the vertex of this quadratic?
(3,-4)
Find the y-intercept of a line that goes through the point (6,0) and has a slope of 1/3.
y-int is -2
What do you call a tree made up of numbers?
Geome TREE...
Use the three equations below OR the table and your calculator to write the equation of a quadratic function that fits this data.
4a + 2b + c=34, 25a + 5b + c=38, 49a + 7b + c=24
time (s) 2 5 7
height (m) 34 38 24
h(t)= -5/3t2 + 13t + 44/3
OR h(t) = -1.67t2 + 13t + 14.7
Make a sketch of the following exponential function. Also state the Domain, Range, y-int, whether the function is increasing or decreasing, and the equation of the Horizontal asymptote.
y = 2(0.8x) - 3
Teacher See Sketch
D: all reals R: y > 3 y-int: (0,-1)
Decreasing HA: y = -3
The path of a golf ball that has been hit can be modeled by the equation: h(t) = 12t - 4t2, where h(t) is the height above the ground in meters since the ball was hit and t is the time in seconds.
How many seconds does it take for the ball to hit the ground?
What is the maximum height reached by the ball?
After 3 seconds the ball hits the ground.
The maximum height reached by the ball is 9 meters
Find the equation of the line that goes through the points (3,2) and (9,-2).
y = -2/3x + 4
OR
y = -.667x + 4
Why shouldn't you let advanced math intimidate you?
Because it's as easy as pi
A quadratic has an axis of symmetry at x=-1/2 and an x-intercept at (2,0). Write the equation of this quadratic in the form f(x) = (x - p)(x - q), and in standard form f(x) = ax2 + bx + c.
f(x) = (x-2)(x+3)
f(x) = x2 + x - 6
Make a sketch of the following exponential function. Also state the Domain, Range, y-int, whether the function is increasing or decreasing, and the equation of the Horizontal asymptote.
y = -2(1.4x) + 1
Teacher See Sketch
D: all reals R: y < 1 y-int: (0,-1)
Decreasing HA: y = 1
Given that a quadratic has an axis of symmetry, x = 1 and goes through the point (-2,4) and has a y-intercept of (0,-1).
y = 0.625x2 - 1.25x - 1
Find the equation of the line that goes through the point (4,5) and is perpendicular to the line that goes through the points (-2,3) and (4,-1).
y = 3/2x - 1
OR
y = 1.5x - 1
What did the MEAN triangle say to the circle?
You're pointless.
Points A and C are as follows (-9,-1) and (3,5).
Find the equation of the line that is perpendicular to line AC and crosses through the midpoint of AC.
Write it in the form ax + by + d = 0, where a, b, and d are in the set of Z.
2x + y + 4 = 0
OR
-2x - y - 4 = 0