Quadratic Formula
Find x (simplify as much as possible):
x2 + 3x - 3 = 0
x =
(-3 + √21) / 2
(-3 - √21) / 2
Using the equation, what is the vertex of this graph and is the parabola facing upwards or downwards?
y = -(x-3)2 - 12
Vertex: (3,-12)
Parabola facing downwards
Using the 3 coordinates (0,0), (6, 24), (14, 0) to describe the start, end, and highest point of the projectile motion of a bomb shot out of the cannon, what is the very highest point at which the bomb reaches?
The vertex is the highest point and since (0,0) and (14,0) are the two points at which the bomb is on the ground, coordinate (6,24) is the highest point of the bomb.
Find the quadratic equation using the factors:
(x + 21)(3x - 2) = 0
3x2 + 61x - 42 = 0
Write the column vector for the transformation of this function:
y = (x-2)2 + 12
(2)
(12)
Find x (simplify as much as possible):
x2 + 8x + 13 = 0
x =
-4 + √3
-4 - √3
Convert the vertex form into standard form:
y = 2(x - 5)2 + 24
y = 2x2 - 20x + 74
What is projectile motion?
The motion in which a parabola shaped-function is formed and where gravity acts on the projectile to bring the object to the ground. Also, there is the maximum height in the motion. (Similar answers are correct as well).
Factor the equation and find the x value(s):
x2 - 576 = 0
(x-24)(x+24) = 0
x = 24, -24
Using the column vector, what is the equation of the function:
(-5 )
( 2 )
y = (x+5)2 + 2
Find x (simplify as much as possible):
3x2 - 8x - 11
x =
11/3
-1
Convert the standard form into vertex form:
y = x2 + 8x + 25
y = (x + 4)2 + 9
A man is standing on a stage and throws a bouquet to the audience, the throw can be modeled by the equation, h(d) = (-3/2)d2 + 3d, where 'd' is distance and 'h' is height.
What is the distance at which the bouquet reaches the audience?
d = 2 units
Factor the equation and find the x value(s):
3x2 + 11x - 20 = 0
(3x - 4)(x + 5) = 0
x = 4/3, -5
Describe the transformation from function f(x) to g(x):
f(x) = x2
g(x) = (x+2)2 + 102
Move 2 units to the left and 102 units up.
Find x (simplify as much as possible):
22x2 + 2x2 + 3 = 0
x =
(-1 + i √65) / 22
(-1 - i √65) / 22
What is the equation for vertex form?
f(x) = a(x-h)2 + k
A golf ball is hit and the path traveled can be expressed by the equation: h(d) = (-1/108)d2 + 4/3d, where 'h' is the height and 'd' is the distance traveled. Find the distance traveled by the golf ball when it finally reaches the ground.
d = 144 units
Factor the equation and find the x value(s):
-32x2 + 8x = 0
-8x(4x - 1) = 0
x = 0, 1/4
Let f(x) = x2 + 4x + 1 and g(x) = 2x2 - x + 4, find the expression for:
(f*g)(x)
What is the quadratic formula?
x = [-b +- √(b2 - 4ac)] / 2a
What do the variables (h,k,& a) in vertex form represent?
'h' represents the x-coordinate of the vertex, 'k' represents the y-coordinate of the vertext, and 'a' represents how much the graph is stretched or shrunk (also tells us if the parabola is upside down).
The coordinates (0,0) and (7,0) are points from the start and end motion of a basketball, what is the highest point that the basketball reaches? (In projectile motion, the parabola should always face downwards.)
Vertex: (7/2, 49/4)
Find the quadratic equation using the x-values:
x = -2, 1/5
5x2 + 9x - 2 = 0
Given f(x) and a transformation, give the new function, g(x):
f(x) = -2(x+3)2 + 12
Compress vertically by a factor of 2, move 18 to the right, move 13 down, and reflect in the x-axis.