Completing the Square
Real World Quadratics
Factoring
Vertex Form
Factoring when a is not 1
100
Solve (x - 3)^2 = 4
x = 1 or 5
100

At the Nets game, an employee shoots a t-shirt out of a cannon. The height of the shirt, h (x), based on the number of seconds, x, is given by the function h(x)=-4x^2+24x+10.

What is the starting height of the t-shirt? Include UNITS!


10 feet
100
What is x^2 + 3x + 2 in factored form?
(x + 2)(x + 1)
100
What is the vertex form of the equation (x + 1)^2 = -9?

(x + 1)^2 + 9 = y

100

Factor 3n^2-2n-5

(3n - 5)(n + 1)
200
x^2 + 4x = 5
x = -5 or 1
200

At the Nets game, an employee shoots a t-shirt out of a cannon. The height of the shirt, h (x), based on the number of seconds, x, is given by the function h(x)=-4x^2+24x+10.

After how many seconds does the t-shirt reach its maximum height?
After 3 seconds
200

What is x^2 + 12x + 32 in factored form?

(x + 4)(x + 8)
200
What is the vertex of the equation y = (x +2)^2 -3
(-2, -3)
200

Factor 2n^2+3n-9

(2n - 3)(n + 3)
300
x^2 - 6x + 7 = 23
x = -2 or 8
300

At the Nets game, an employee shoots a t-shirt out of a cannon. The height of the shirt, h (x), based on the number of seconds, x, is given by the function h(x)=-4x^2+24x+10.

What is the t-shirt's maximum height in feet?
46 feet
300
What are the solutions to (x + 6)(x + 3) = 0?
x = -6, x = -3
300
An equation is written in vertex form y = a(x - h)^2 + K, such that y = 3(x + 3)^2 - 6. What are the values of a, h, and k?
a = 3

h = -3
k = -6

300

Factor  2x^2+11x+5

(x + 5)(2x + 1)
400
x^2 + 16x + 20 = -8
x = -2 or 14
400

The amount of fans in a stadium, y, is based on the number of hours, x, into the game. This can be represented by the equation y=-100x^2+400x+5,000.

How many fans are in the stadium at the start of the game?

5,000 fans
400
What are the solutions to x^2 + 10x + 12 = 3?
x = -9, x = -1
400
Convert the following to vertex form:

y = x^2 + 2x - 6

y = (x + 1)^2 - 7
400

Factor 2n^2+5n+2

(2n + 1)(n + 2)

500
2x^2 + 6x + 2 = -2
x = -2 or -1
500

 The amount of fans in a stadium, y, is based on the number of hours, x, into the game. This can be represented by the equation y=-100x^2+400x+5,000.

After the game, the Fire Marshall fined the stadium owner and said, “The maximum occupancy of our stadium is 5,500. You exceeded the maximum occupancy.” What would you say to the Fire Marshall if you were the stadium owner?
(Time limit extension - 5 min MAX)

Incorrect! The vertex is the maximum of the function, and is represented by the coordinate pair (2, 5,400). This shows a maximum of 5,400 fans, not 5,500 so the fire marshall is incorrect.
500
What is the standard form of the equations whose solutions are x = 2 and x = -3?
x^2 + x - 6
500
Convert the following to vertex form: y = 2x^2 + 8x +9
y = 2(x + 2)^2 + 1
500

Factor 2x^2-11x+15

(2x - 5)(x - 3)
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