Solve for X
What is the quadratic formula?
x= negative b plus or minus the square root of b squared minus four-a-c, all over two a.
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
What are the coordinates of the vertex? Which two letters and in which order?
(h, k)
A function has zeroes 1 and 2. At which x values is y along the x-axis?
x = 1 and 2.
What is the formula for the discriminant of a function?
b2 - 4ac
What is the capital city of Germany?
Solve using the quadratic formula: 0 = x2 - 2x - 8
x = -2 and x = 4
What does the vertex tell us about the graph of a function?
The minimum or maximum.
Where the function changes from increasing to decreasing or vice-versa.
A function has zeroes -3 and 4. Write the function as a product of two binomials.
0 = (x + 3)(x - 4)
How can we use the discriminant to find the number of solutions to a quadratic function?
If positive, two solutions. If negative, no solutions. If zero, one solution.
What is the oldest continuously inhabited city in the United States?
Saint Augustine
Solve for x.
(x-3)2 = 0
x = 1
What is the equation for the axis of symmetry and which coordinate, x or y, of the vertex does it correspond to?
h = -b / 2a
(x - 5)(x - 6)
x2 - 11x + 30
Find the discriminant for x2 + 4x + 3.
Name the four constituent countries of the United Kingdom.
England, Wales, Scotland, Northern Ireland.
Solve by completing the square: 5 = x2 + 6x
x2 + 6x + (6/2)2 = 5 + (6/2)2
x2 + 6x + (3)2 = 5 + 9
(x + 3)2 = 14
x + 3 = plus or minus sqrt(14)
x = 3 + sqrt(14) OR x = 3 - sqrt(14)
A company's profits are modeled by the function
f(x) = -2x2 + 12x + 22 , where x represents the time in years since the company's founding and f(x) the profit that year. In which year did the company make the most money?
h = -(b / 2a), or 3
A function has zeroes 7 and 8. What are three possible values of a, b, and c?
a = 1, b = -15, c = 56
How many solutions does 0 = 5x2 + 8x - 3 have?
Two.
Who was the king of the Roman Gods?
Jupiter
Solve for x: 0 = x2 + 4x + 6
no real solutions
A company's profits are modeled by the function
f(x) = -2x2 + 12x + 22 , where x represents the time in years since the company's founding and f(x) the profit that year. How much money did the company make in their most profitable year?
h = 3
f(h) = 40
A quadratic function has zeroes p and q. Write it as the product of binomials.
(x - p)(x - q)
How many solutions does -2x2 - 3x - 4 have?
None.
Who was the first king of England?
William I "The Conqueror"