Describing Quadratics
Completing the Square
Quadratic Formula
Discriminant
Word Problems
100
Does the Following Quadratic Open UP or DOWN?
y = -3(x + 4)2 - 6
DOWN
100
Find the vertex form of f(x) = x2 − 8x + 15 by completing the square.
f(x) = (x - 4)2 =1
100
Is this quadratic formula?
Yes
100
Where does b2−4ac come from?
Quadratic Formula
100
What form do you need to put your equation in when the word problem states: "hit the ground" ?
Factored
200
If a Parabola is open DOWNWARD and has an X-intercept at 0 and 6; What is it's Axis of Symmetry?
X = 3
200
Find the vertex form of f(x) = x2 - 20x +19= 0 by completing the square.
(x - 10)2 - 81
200
Solve 6x2 + 12x = 90 using the quadratic formula.
x= -5 and 3
200
What does the discriminant tells us?
The discriminant indicates whether there are two solutions, one, or none at all
200
What form do you need to put your equation in when the words maximum or minimum is used in a word problem?
VERTEX
300
What does standard and vertex form tell you about a quadratics?
Standard: opening up or down and y-int
Vertex: opening up or down and vertex (max/min)
300
What is the vertex of the following: f(x) = x2 + 4x +14 Solve by completing the square.
Vertex: (-2, 10)
300
Solve x2 - 8x + 14 = 0 using the quadratic formula.
x = -(-8) ±√ (-8)2 - 4(1)(14) / 2(1)
= 8 ±√ 8 / 2
= 5.41 and 2.59
300
Find the discriminant to determine the number of roots in the equation x2 + 6x - 5 = 0
x2 + 6x - 5 = 0
62 - 4(1)(-5)
= 56
It has 2 distinct roots
300
An arrow is shot off a cliff and into the ocean while following the path of the equation:
y = -4x2 + 24x + 18 (x= time y=height in feet)
What is the height of the arrow after 4 seconds?
50 feet
400
What is the vertex of the Following Quadratic and is it a MAX or MIN:
Y = -4(X - 3)2 + 1
Vertex: (3, 1)
MAX
400
What is the vertex of the following: f(x) = 2x2 − 8x − 3. Solve by completing the square.
Vertex: (2, -11)
400
Solve x2 + 4x - 21 = 0 by using quadratic formula.
x = 3 or -7
400
A group of kids doing a science project are shooting bottle rockets into the air. The height in meters of a rocket that was shot straight up into the air with a velocity of 45 m/s is given by h = -9.8t2 + 45t +1.2. Will the bottle rocket reach a maximum height of 64.5 meters? Use the discriminant to find your answer.
64.5 = -9.8t2 + 45t +1.2
0 = -9.8t2 + 45t - 63.3
452 -4(-9.8)(-63.3)
= - 456.36
No, it won't reach the maximum height of 64.5
400
The equation P=-3x2+12x+2 represents the amount of P profit for the x cost of an item. What is the maximum profit for the sale of the item?
$14
500
What is the Axis of Symmetry of the following Quadratic:
Y = -0.5(X - 4)2 - 4
X = 4
500
What is the vertex of the following: x2 - 6x + 6 = -1
Vertex: (3, -2)
500
Solve 2x2 = 7x + 6 by using quadratic formula.
x = -(-7) ±√(-7)2 -4(2)(-6) / 2(2)
x = (7 ±√ 97) / 4
x =4.21 and -.71
500
Find the value of k for which 2x2 - 6x + k = 0 has one distinct root.
2x2 - 6x + k = 0
-62 - 4(2)(k) = 0
36 - 8k = 0
-8k = -36
k = 8/36
500
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?
1.43 sec