Put into Vertex form
f(x)=x2-2x-3
Put into vertex form.
ID the vertex.
Sketch a graph.
f(x)=(x-1)2-4
Vertex = (1, -4)
f(x)=x2+6x+9
y-int: (0,9)
x-int:(-3,0)
The sum of a number and its reciprocal is 29/10. What are the numbers?
2/5 and 5/2
The equation h(t)=-16t2+198t+25 represents the height of a diver jumping off a cliff after t seconds. What is the height of the diver after 5 seconds?
615 ft.
f(x)=-x2-4x+5
Put into vertex form.
ID the vertex.
Sketch a graph.
f(x)=-(x+2)2+9
Vertex = (-2, 9)
Left 2, up 9, reflected across the x-axis
f(x)=-x2-7x+8
y: 8
x: 1, -8
The vertex of f(x)=ax2+6x+c is (3, 11). Find a and c.
a=-1, c=2
A ball being thrown in the air can be modeled by the equation h=-4.9t2+14t+49. where h represents height in feet and t represents time in seconds. How long does it take for the ball to reach its maximum height? (OK if not simplified)
1.43 sec
(14/9.8)
f(x)=x2-4x+1
Put into vertex form.
ID the vertex.
Sketch a graph.
f(x)=(x-2)2-3
Vertex = (2, -3)
f(x)=2x2-18
x-ints:(3,0),(-3,0)
y-int: (0,-18)
A square piece of cardboard is used to construct an open box by cutting 3-inch squares out of each corner and turning up the flaps. Find the size of the original square if the resulting box has a volume of 243 cubic inches.
15in by 15in
The function h(t)=-15t2+60t+3 represents the height of a water balloon at t seconds. How long will it take for the water balloon to hit the ground?
about 4.05 seconds
(10+rt(105))/5
f(x)=-3x2-6x+7
Put into vertex form.
ID the vertex.
Sketch a graph.
f(x)=-3(x+1)2+10
Vertex = (-1, 10)
Left 1, up 10, reflected across the x-axis, vertically stretched by 3
f(x)=2x2+3x-5
x-ints: (-2.5,0),(1,0)
y: (0,-5)
Three rectangular corrals are to be made form 200 yards of of fencing. If the builders of the fence want to maximize the total area, what dimensions should be used to make the corrals.
25 yds by 50 yds
The equation P=-3x2+12x+2 represents the amount of P profit for the x cost of an item. What should the price of the item be to maximize profits? What is the maximum profit for the sale of the item?
Price: $2
Profit: $14
f(x)=-x2+6x-9
Put into vertex form.
Describe the transformations to the parent function.
f(x)=-(x-3)2
Right 3, Reflected across the x-axis.f(x)=3x2+4x-4
x-ints: (2/3,0)(-2,0)
y: (0,-4)
Find the value of m in the function
f(x)=mx2+(m-1)x+(m+2)
if the maximum value of the function is 2.
m=-1
h(t)=-16t2+64t+80 represents the height of a rocket at t time in seconds. When will the rocket be 100 ft in the air?
.34 seconds and 3.66 seconds
(4+/-rt(11))/2