Factoring
Factor the following: x2 - 121
(x + 11)(x - 11)
The y - intercept of the graph of a quadratic in Standard form is which variable?
What is C?
What would the equation of a quadratic in Vertex form look like if a = -2, h = 6, and k = -12?
y = -2(x - 6)2 - 12
What is the quadratic formula?:
x=(-b±√(b^2-4ac))/2a
Find the vertex of
y = 4(x-5)2 + 7
(5,7)
The Wright brothers tried for months to perfect the art of flying. During their attempts they would send their plane off of a small cliff to help get air time. To model one of their attempts, we can use the formula below. Assume time is in minutes and height is in feet. What was the initial height of the cliff?
h=-4t^2 +7t+30
30 feet
Factor the following:
x2 -5x-50
(x -10)(x + 5)
What equation is used to find the "x" value of the vertex in standard form?
x = -b/2a
Re-write the following equation in Vertex Form:
y = x2 +14x - 3
y = (x + 7)2 - 52
Solve using the quadratic formula:
4x2 + 5x - 9 = 0
What is x = 1 or x = -9/4
Find the vertex of
y = x2 - 2x
(1,-1)
The Wright brothers tried for months to perfect the art of flying. During their attempts they would send their plane off of a small cliff to help get air time. To model one of their attempts, we can use the formula below. Assume time is in minutes and height is in feet. How long did it take for the plane to reach it's maximum height?
h=-4t^2 +7t+30
7/8 or 0.875 minutes
Factor the following:
4x2 - 6x
2x(2x - 3)
If you are factoring...
1) What feature are you solving for?
2) What do you do with your factors to actually solve?
1) The X-Intercepts
2) Set the factors equal to ZERO
Re-Write the following equation in Standard Form:
y = -3(x +3)2 + 15
y = -3x2 - 18x - 12
Describe the nature of the solutions for the following:
y = 4x2 - 10x + 7
0 real solutions
(2 imaginary solutions)
Find the vertex of
y=-x2+8x-15
(4,1)
The Wright brothers tried for months to perfect the art of flying. During their attempts they would send their plane off of a small cliff to help get air time. To model one of their attempts, we can use the formula below. Assume time is in minutes and height is in feet. What was the maximum height of the plane?
h=-4t^2 +7t+30
33.0625 feet
Factor the following:
2x2 - 8x - 90
2(x-9)(x+5)
Which variable in the Vertex Form of a quadratic can tell you if the vertex will be a minimum or a maximum point?
What is a?
Re-write the following equation in Standard form:
y = 2(x + 7)2 - 36
y = 2x2 + 28x + 62
Solve using the quadratic formula:
x2 + 3x + 9 = 0
What is x =
(-3+-3isqrt(3))/2
Find the vertex of
y = -(x + 4)2 +2
(-4,2)
The Wright brothers tried for months to perfect the The Wright brothers tried for months to perfect the art of flying. During their attempts they would send their plane off of a small cliff to help get air time. To model one of their attempts, we can use the formula below. Assume time is in minutes and height is in feet. How long was the plane in the air before landing on the ground?
h=-4t^2 +7t+30
3.75 minutes
Factor the following:
3x2 - 11x + 10
(3x-5)(x-2)
The Axis of Symmetry always goes through what point on a parabola?
What is the Vertex?
(x=h)
Re-write the following equation in Vertex Form:
y = 3x2 - 12x + 8
y = 3(x - 2)2 - 4
Solve using the quadratic formula:
2x2+4x-9=0
(-2+-sqrt(22))/2
Find the vertex of
y = -4x2 + 4x + 3
(1/2, 4)
The Wright brothers tried for months to perfect the art of flying. During their attempts they would send their plane off of a small cliff to help get air time. To model one of their attempts, we can use the formula below. Assume time is in minutes and height is in feet. How long did it take the plane to reach a height of 15 feet?
h=-4t^2 +7t+30
What is 3 minutes