Features of parabolas
Does the following parabola open upward or downward? What is the y-intercept?
y=2x2+12x+11
Upward and y=11
What is the increasing and decreasing interval of the parabola
y=-x2+4x-3
I: (-infinity, 2) D: (2, infinity)
A toy rocket is launched from the top of a 48-foot hill. The rocketβs initial upward velocity is 32 feet per second and its height h at any given second t is modeled by the equation π(π)=βπππ2+πππ+ππ.
What time did the rocket reach maximum height?
1 second
The length of a rectangle is 2 units more than the width. The area of the rectangle is 24 square units. What is the width, in units, of the rectangle?
w=4
NO CALCULATOR
What is the vertex of the parabola?
y=-x2+4x-3
(2, 1)
What is the increasing and decreasing interval of the parabola
y=x2+4x+3
D: (-infinity, -2) I: (-2, infinity)
A toy rocket is launched from the top of a 48-foot hill. The rocketβs initial upward velocity is 32 feet per second and its height h at any given second t is modeled by the equation π(π)=βπππ2+πππ+ππ.
How long was the rocket in the air?
3 sec
The width of a rectangle is 3 units less than the length. The area of the rectangle is 40 square units. What is the width, in units, of the rectangle?
W=5
NO CALCULATOR
What are the zeros of the parabola?
y=-x2+4x-3
x=1 and x=3
What interval is the parabola negative?
y=x2+4x+3
(-3, -1)
A toy rocket is launched from the top of a 48-foot hill. The rocketβs initial upward velocity is 32 feet per second and its height h at any given second t is modeled by the equation π(π)=βπππ2+πππ+ππ.
How high was the rocket at 2 seconds?
48ft
The length of a rectangular poster is 9 more inches than three times its width. The area of the poster is 30 square inches. Solve for the dimensions (length and width) of the poster.
w=2, l=9
NO CALCULATOR
What is the equation for the axis of symmetry of the parabola?
y=-x2+4x-3
x=2
What interval is the parabola positive?
y=x2+4x+3
(-infinity, -3) and (-1, infinity)
NO CALCULATOR
A toy rocket is launched from the top of a 48-foot hill. The rocketβs initial upward velocity is 32 feet per second and its height h at any given second t is modeled by the equation π(π)=βπππ2+πππ+ππ. What was the maximum height of the rocket?
64ft
NO CALCULATOR
The width of a rectangle is 3 units less than the length. The area of the rectangle is 28 square units. What is the length, in units, of the rectangle?
7
Compare f(x)=-x2+10x+1 and g(x) shwon in the table below
x: 0, 1, 2, 3, 4
g(x): 2, 5, 6, 5, 2
Find the difference in the maximum y-values.
26-6=20
Determine the behavior of the graph from -3<x<-2
y=x2+4x+3
Negative and decreasing
NO CALCULATOR
A frog sitting on a stump 5 feet high hops off and lands on the ground. During her leap, the frogβs height h in feet is given by the equation π(π)= βπ 2+π +5, where d is the horizontal distance in feet from the base of the stump.
After how many seconds did the frog hit the ground?
3 seconds
No Calculator
The length of a rectangular poster is 5 more inches than two times its width. The area of the poster is 33 square inches. Solve for the dimensions (length and width) of the poster.
w=3, l=5