VERTEX FORM OF QUADRATICS
What is the vertex of the graph of the function f(x)=x2+10?
(0,10)
** Find the graph of a pumpkin launched from a 10-ft tower that is modeled by the equation y=-16t2+32t+10.
A
Solve the equation x2 - 18x - 40=0
x=-2, 20
Solve x2 = - 100
x = -10i, and 10i
Solve 0 = x2 + 8x + 17 (by completing the square)
x = -4 + i or x = - 4 - i
Function "g" is a transformation of f(x) = x2. The graph of "g" is translated right 5 units and up 1 unit of the graph of f.
What is the equation?
g(x)=(x-5)2+1
What is the maximum height of a pumpkin launched from a 10-ft tower that is modeled by the equation y=-16t2+32t+10.
(1 sec,26 feet)
A ball is thrown from the top row of seats in a stadium. The function h(t)= - 16t2 + 16t + 96 gives the height, h, in feet, of the ball t seconds after it is thrown. . . . How long will it be when the ball hits the ground?
t = -2, 3, .. . .3 seconds
Multiply (3 + 3i)(3 - 3i)
18
Which statements are true for, (select all that apply):A. The graph opens downward B. The range of the function is all real numbers C. The equation is y = (x + 1/2)2 + 3/4 D. The graph of the function has a minimum of y = 3/4 at x = -1/2
C and D
Function "g" is a transformation of f(x) = x2. The graph of "g" is translated right 5 units and up 1 unit of the graph of f.
What is the equation in standard form?
g(x)=x2-10x+26
A toy cannon ball is launched from a cannon on top of a platform. The equation h(t) = -5t2 + 30t + 8 gives the height h, in meters of the ball 2 seconds after it is launched. What equation can be used to tell if the ball reaches the height of 34 m?
-5t2 + 30t + 8= 34
Identify the interval where the function is positive: y = -x2 + 5x + 14
-2 < x < 7
Do the division 25 / (4 + 3i)
4 - 3 i
Solve x2 - 4x+13=0
x= 2 + 3i or x = 2 - 3i
What is the equation written in vertex form of a parabola with a vertex of (-5,-4) that passes through (-7,8)?
f(x)=(3x+5)2-4
Find the regression for the graph of the volleyball with the points (0,32.4), (10, 20.1), (20, 5.8) (40, 75.6) (round decimals to the nearest hundredth)
y = 0.11x2 - 3.36 x + 35.24
Solve x2 + 5x + 1 = 0
x = - 5/2 + and - square root 21/ 2
A toy cannon ball is launched from a cannon on top of a platform. The equation h(t) = -5t2 + 30t + 8 gives the height h, in meters of the ball 2 seconds after it is launched. Does the ball reach a height of 34 m?
Yes, maximum height is 19 m at 3 seconds