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Factor
Solve
Interpretation
Miscellaneous
Key Vocab
100
Rewrite x^2 - 2x - 3 as a product of binomials.
(x-3)(x+1)
100
Solve x^2=5x-10
No Solution
100
You throw a basketball into the hoop. The height h (in feet) of the ball after t seconds can be modeled by the equation h =-16t^2 + 24t + 4. Based on the equation, what is the initial height of the ball. EXPLAIN AND JUSTIFY!
The initial height of the ball is 4 feet because our CONSTANT tells us our Y-INTERCEPT or INITIAL STARTING HEIGHT. The constant in this equation is 4 feet, therefore the initial starting height of the ball is 4 feet.
100
What are the four components every graph needs before actually plotting the points?
Table of values, arrows, labels of axes/function, proper scale
100
What is a vertex of a quadratic?
Turning point on a graph
200
Factor x^2 + 10x + 25. What method did you choose and why?
(x+5)^2. Factor using perfect squares because 25 is a perfect square, and 5+5=10 which is our b value.
200
Solve -9=x^2-6x
x=3
200
You throw a basketball into the hoop. The height h (in feet) of the ball after t seconds can be modeled by the equation h =-16t^2 + 24t + 4. Explain and justify what the vertex (0.75, 13) means in the context of the problem.
The vertex (0.75, 13) means that the ball reached its maximum height of 13 feet at 0.75 seconds.
200
What strategy can we use to convert a function from standard form to vertex form?
Completing the Square
200
What is the difference between standard form and vertex form of a quadratic?
Standard form: y=ax^2+bx+c; vertex form: y=a(x-h)^2+k
300
Factor completely 5r^2 - 80
5(r^2 - 16). 5(r - 4)(r + 4)
300
Solve using any method 2x^2 - 3x - 5 = 0
{5/2, -1}
300
A coin falls off of a building. The height h (in feet) of the coin after t seconds can be modeled by the equation h =-16t^2 + 96t + 112. Explain and justify what the point (7, 0) represents in the context of the problem.
The point (7, 0) is a root/zero/solution/x-intercept of the graph. This point represents that the coin was at a height of 0 ft (hit the ground) at 7 seconds.
300
Ms. Negron is reorganizing her classroom. The length of the room is represented by 4 less than twice a number, and the width of the room is the same number n. Write let statements that support this scenario.
Let n represent the width of the classroom. Let 2n-4 represent the width of the classroom.
300
What do "let" statements tell us? Give an example.
Let statements tell us what our variables / unknowns represent. For example, let x represent an unknown number.
400
Factor by grouping 2x^2+6x-x-3
(x+3)(2x-1)
400
Solve by completing the square x^2 + 6x + 8 = 0
{-2, -4}
400
You are building a shed. The dimensions of the shed are (x-2) ft., (x+6) ft., and (x-1) ft. If the volume of the shed is 60 ft^2, we get three solutions of x=4, x=-4, and x=-3. Can we use all of these solutions for x? Explain and justify your response.
We cannot use all three solutions for x. We can only use x=4, because when you substitute x=-4 and x=-3 you would get a negative length which is invalid, so we would have to omit those values for x.
400
Ms. Negron is reorganizing her classroom. The length of the room is represented by 4 less than twice a number, and the width of the room is the same number n. If the area of the room is 30 square feet, determine the length and width of the classroom.
30=(2n-4)(n). 30=2n^2-4n. 0=2n^2-4n-30. Solutions are n=-3, n=5. Omit n=-3 because you cannot have a negative length.
400
How do we write the x-intercepts x=4, x=-10, and x=12 as a solution set?
{-10, 4, 12}
500
Factor 16b^2 + 60b − 100
4(b + 5)(4b − 5)
500
Factor using quadratic formula 9n^2 = 4 + 7n
{7 + square root 193/18, 7 − square root 193/18}
500
Ms. N has a business. Her profit is represented by y=-16x^2+20x+15, where y is the amount of profit in thousands of dollars, and x is the number of years since 2000. Explain what the two points (13, 46) and (14, -186) represent in the context of the problem. What happens between these two points?
(13, 46) represents in 2013 Ms. N will have a profit of $46,000, and in 2014 Ms. N will lose $186,000. Between these two points, Ms. N loses money and probably goes out of business.
500
What is the GCF of −6a^2 − 25a − 25. Then factor.
GCF is -1. To factor, we would get −(2a + 5)(3a + 5).
500
Name ALL 15 key features/characteristics of a graph.
Table of values, vertex, axis of symmetry, x-intercepts, y-intercept, concavity, maximum/minimum, domain, range, increasing interval, decreasing interval, dilation, reflection, vertical shift, horizontal shift