Quadratic Functions, vertices and their Solutions
What is the vertex of a quadratic?
The vertex is either the minimum or maximum point on a quadratic.
What are you looking for when you are asked to solve a system of equations?
You are looking for the point or points of intersection of two or more graphs.
What is the formula for average rate of change?
change in y/ change in x
What is the parent function of y = 2x2 +5?
y = x2
What is i? i2? i3? i4?
i is the square root of -1
i2 is -1
i3 is -i
i4 is 1
What does it mean to find the roots, solutions, or zeros of a quadratic?
It means to find the point(s) of x-intercepts.
How do you determine how many points of intersection there are in a quadratic system of equations?
You can use the quadratic formula (specifically the discriminant) to find how many points of intersection(s) there are. Negative is none, zero is one, and positive are two.
What is the rate of change during the interval 1-4 hours if a car traveled 12 mi in the first hour and 16 mi in the forth hour?
4/3 mi per hour or 1 1/3
If a function, f(x) is translated f(x- 5), how is the graph transformed?
The graph is moved to the right 5 units
4
Does this quadratic have a minimum or maximum?
f(x) = x2 +4x - 5
This quadratic has a minimum because "a" is positive.
What is the solution(s) to the system of equations y=x2 -x-20 and y=3x-15?
The solutions are (-1,-18) and (5,0)
If from 4 -7 pm it snowed 10 in and from 9- 11pm it snowed 11 in, which interval has a greater rate of change?
9 -11 pm with a rate of change of 5.5
What is the one thing Dina hates most?
TAXES
What is the sum of (7 + 3i) and (-8 +9i)?
-1 +12i
The roots of the equation x2 +2x +5=0 are
-1 -2i and 1 +2i
What is the solution(s) to the system of equations shown below?
x2 + y2 = 20
y= x - 6
The solutions are (4,-2) and (2,-4)
Calculate the average rate of change from 3 to 9 seconds, in feet per second if a table shows a bird's height during flight to be 6.26 ft in 3 seconds and 3.41 ft in 9 seconds.
-0.475 ft per second
If a function is y =-3x2, how is it transformed compared to its parent function y =x2?
It is downward facing and narrower.
Simplify the following expression:
(3k-2i)2
9k2 - 12ki + 4
What is the vertex of the following quadratic?
4x2 + 6x - 3
The vertex is (-3/4, -5 1/4) or (-0.75, -5.25)
True or False: Rachael is from Ohio
FALSE!
State the average rate of change for the distance traveled between hours 2 and 4. Include appropriate units if a table shows a family traveled 112 mi from home after 2 hours of travel and 238 mi after 4 hours of travel.
63 mph
The point (2,-3) lies on the graph of the equation y =f(x). What point must lie on the graph of the equation y= f(x - 4) +1?
(6, -2)
Express (1-i)3 in a+bi form.
-2 - 2i