Formulas
What is the formula for the axis of symmetry?
- b / 2a
What is the domain of all the graphs?
All real numbers
y = 2x2 + 4x
Vertex (-1, -3)
Find the A.O.S and Vertex
1/2(x-4)2
x = 4
(4,0)
The height in feet of a dolphin as it jumps out of the water at an aquarium show can be modeled by the function f(x) = -16x2 +32x whee x is the time in seconds after it exits the water. Find the maximum height and the time it take to reach the maximum height. Then find how long the dolphin is in the air.
Max Height (1, 16)
Time to reach height 1 second
Time in air 2 seconds
How do you find the y-value of the vertex assuming you have already found the x-value?
By using the x-value and plugging it back into the equation.
What is the vertex?
The max/min of the graph
Find the Vertex
y = 3x2 -6x +5
Vertex (1, 2)
Find the AOS and Vertex
y = -2(x + 2) + 3
x = -2
(-2,3)
The height in feet of a soccer ball that is kicked can be modeled by the function f(x) = -8x2 + 24x where x is the time in seconds after it is kicked. Find the soccer ball's maximum height and the time it takes the ball to reach this height. Then find how long the soccer ball is in the air.
Max Height (1.5, 18)
Time to reach max height 1.5 seconds
Time in air 3 seconds
What is standard form?
ax2 + bx + c
What line goes through the vertex?
Axis of symmetry
Graph y = 4x2 and identify the following parts
Vertex:
A.O.S:
Max/Min:
Vertex: (0,0)
A.O.S.: x = 0
Min
Graph and label the AOS and vertex
y = 2(x + 1)2
x = -1
(-1,0)
Joe hit a golf ball that had the equation
h(t) = -16t2 + 128t
t is in seconds and h is in feet. How long did the golf ball take to reach the maximum height and what is the maximum height of the golf ball?
time = 4 seconds
height = 256 ft
What is vertex form?
y = a(x-h)2 + k
How/What determines the range?
Give an example for each situation.
If the point is a max or min
max --> y is less than the y-value of the vertex
min --> y is greater than the y-value of the vertex
Graph y = x2 - 2 and Identify the following
Vertex:
A.O.S.
Max/Min
Vertex: (0,4)
A.O.S. x = 0
Min
Graph and label the AOS and vertex
y = (x - 3)2 + 2
x = 3
(3,2)
What parts of the vertex form give us the vertex?
How do we know if x is positive or negative?
h and k
if the formula still has a negative sign then it is positive.
If the formula has a positive sign then it is negative.
What are the zeros? Write two other words for zeros of quadratic equations.
solutions, x-intercepts
Graph y = -2x2 + 8x + 2 and Identify the following
Vertex:
A.O.S
Max/Min
Vertex (2, 10)
A.O.S x = 10
Max
Graph and label the AOS and vertex
y = 3(x + 2)2 - 1
x = -2
(-2,-1)