Opens? Y-Intercept
X-Intercepts
Axis of Sym. and Vertex
Graphs and Equations
Min./Max Quadratics Sol.
100
State whether the parabola opens up or down and find the y-intercept:
y=x2+3x+9
Open up, (0,9)
100
How many x-Intercepts does the following function have?
y=-2x2+4x+1
Two X-Intercepts
100
What does the graph of an axis of symmetry, for example the line x=3, look like?
Straight Vertical Line
100
Write the quadratic equation of the graph given below in vertex form.
y = 2/3 (x - 3)2 + 1
100
Solve for x by taking square roots:
2(x-1)2-7=3
x=1+/- squareroot(5)
200
State whether the parabola opens up or down and find the y-intercept:
y=-3x2+7x-5
Open Down, (0,-5)
200
Find the x-intercepts of the function:
y=2x2-2x-5
(1+sqaureroot(11)/2,0) and (1-sqaureroot(11)/2,0)
200
What is important about the axis of symmetry?
It is the line across which the parabola is symmetrical, or a mirror image of itself.
200
Find the y-int., the AOS, the vertex and the approximate roots of this function:
(0, -2)
x = 0
Vertex: (0, -2)
Roots={-1.5, 1.5}
200
Solve by completing the square:
3x2 + 18x - 63 = 0
x= -3 + sqroot of 30 and
x= -3 - sqroot of 30
300
State whether the parabola opens up or down and find the y-intercept:
y=-x2+4
Open Down, (0,4)
300
Find the X-Intercepts of the function:
y=4x2-5x-6
(-3/4,0) and (2,0)
300
Find the axis of symmetry for the following function:
y=x2-3x+4
x=3/2
300
Graph the following function:
y=x2 - 2x - 8
,7/2)
300
Solve by completing the square:
x2+6x-3=0
x=-3+/- 2squareroot(3)
400
State whether the parabola opens up or down and find the y-intercept:
y=2x2
Open Up, (0,0)
400
Find the x-intercept(s) of the function:
y=4x2-12x+9
(3/2,0)
400
Find the axis of symmetry and the vertex of the following function:
y=-4x2+8x-9
Axis of Symmetry: x=1
Vertex: (1, -5)
400
Write the equation of the parabola given below in vertex form.
y= -1/3(x - 1.5)2 + 3
400
A factory produces shoes. They want to determine the number of pair of shoes that will maximize their revenues and they have asked you to do it for them. The factory uses the model
r(s) = -18x2 + 117000x - 2865500.
a) Determine the number of pairs of shoes they need to produce.
b) Determine the maximum revenue they will receive.
a) 3250 pairs of shoes
b) They will receive $282,322,000
500
State whether the parabola opens up or down and find the y-intercept:
y=-3x2+2x
Open Down, (0,0)
500
Give an example of a quadratic function that has no x-intercepts.
-
500
Find the vertex of the function:
y=2x2-2x+4
(1/2,7/2)
500
Graph the equation y = -x2 + 4x - 3
500
An object is thrown from a cliff that is 3250 feet high. Its fall follows the model
y=-16t2 - 192t + 3250 .
a) How many feet will it fall between 3 and 4 seconds?
b) After how many seconds does it hit the ground?
Figure it out!!