Discriminant
Choose the Best Model
Comparing Models
Quadratic Formula
Vocabulary
200
If a discriminant is positive you have ______________ solutions
If a discriminant is negative, you have ____________ solutions
If a discriminant is zero, you have ________________ solutions
If a discriminant is positive you have 2 real solutions
If a discriminant is negative, you have zero real solutions.
If a discriminant is zero, you have one real solution
200
Which function best models the data?
Word bank - Quadratic, Exponential, Linear
Quadratic
200
True or False: Function 1 and 2 are both decreasing
True - Function 1 decreases going from left to right
200
Why do we use the quadratic formula?
What is the quadratic formula?
Why do we use the quadratic formula?
To find solutions of quadratic functions
What is the quadratic formula?
200
Define domain and range
Domain: all possible x values
Range: all possible y values
400
Provide a discriminant that has no real solutions
Answers may vary, but must be negative
400
Which function would best represent the scenario below?
A roller coaster descends from the top of a hill, reaches the lowest point of the track, and then climbs back up the next peak.
Quadratic
400
True or False: Function 1 and 2 have the same y-intercept
True (0,3)
400
Find the discriminant and plug into the quadratic equation
Discriminant:
-11
In the quadratic formula
(-3+- squareroot -11)/(2(5))
400
What is slope? What is another name for it?
m = (y_2 - y_1)/(x_2 - x_1)
Rate of change
600
Sketch a graph with a positive discriminant
Ex (answers may vary - needs 2 x-intercepts)
600
Which function would best represent the scenario below?
A gym membership starts at $30 a month and increases by $5 each year due to rising maintenance cost.
Linear
600
Does function 3 have a maximum or minimum? Explain how you know.
Maximum - a value is negative
600
What are the solutions to the desmos quadratic below, use DESMOS
Graphing
x = -1.5 and x= 3.5
600
What is an x-intercept? What are other words for it
x-intercept = when function crosses x-axis
zero, solutions, roots
800
Sketch a graph with a negative discriminant
Answers may vary, but can't have any x-intercepts
800
Which function would best represent the scenario below
A small tech startup begins with 10 users, and the number of users multiplies by 2 every month as word spreads.
Exponential
800
True or False: The domain for function 3 is all real numbers
True - domain is always all real numbers for quadratics
800
Find the solutions of the quadratic formula
Discriminant:
77
Answers for quadratic formula:
x = -20.66 and x = .63
800
What is the difference between a linear, exponential and quadratic function?
Linear - constant rate of change (1 difference)
Exponential - multiply or divide
Quadratic - 2nd difference is constant
1000
Sketch a graph with a discriminant of 0
Answers may vary, but the graph can only have 1 x-intercept
1000
Linear - data is closest to line of best fit
1000
What kind of function is function 2? How do you know?
Exponential - divide by 2 each time
1000
Find the solutions of the quadratic below using the quadratic formula
Once changing the formula to equal zero:
x^2 - 7x + 13 = 0
Discriminant:
-3
Answers to quadratic formula:
None, as discriminant is negative
1000
Free points
Free points