Function Families
Domain is (-∞, ∞) and Range is limited by the vertex, either a maximum OR minimum. Can model projectile motion, profit/cost over time, deep sea diving.
What are Quadratic Functions?
Roots, Solutions, and Zeroes all refer to this key feature on our coordinate plane.
x-intercepts
This key feature can be found from the c-value of Quadratic Functions in Standard Form: ax2 + bx + c.
y-intercept
f(x) = -7.5x2 + 15x + 7.5 represents the path of the basketball for a floater taken by Trae Young of the Atlanta Hawks where x represents seconds the ball was in the air and y represents height of the ball in feet.
This point on the graph represents the initial height of the basketball when Trae Young shot it towards the hoop.
What is the y-intercept?
Domain and Range both limited by the vertex (starting point) which forms a line moving in only one direction. Can model braking/stopping, statistical deviations, and solving Quadratics.
What are Square Root Functions?
We could expect the function: C(x) = -2(x - 3)2 + 2 to have a vertex located in this quadrant.
What is Quadrant I?
This feature can be found from Intercept Form:
y=a(x - p)(x - q)
What are the x-intercepts?
f(x) = -7.5x2 + 15x + 7.5 represents the path of the basketball for a floater taken by Trae Young of the Atlanta Hawks where x represents seconds the ball was in the air and y represents height of the ball in feet.
This point on the graph represents the maximum height of the ball.
What is the y-value of the vertex?
Exponential, Logarithmic, and Rational functions often experience this reaction to flu season.
Asympto-matic
Domain is limited by a vertical asymptote and Range is (-∞, ∞). Can model seismic activity in earthquakes, sound, and light.
What are Logarithmic Functions?
We could expect the function: C(x) = -2(x - 3)2 + 2 to have these kinds of roots.
What are 2 real roots?
This form of Quadratic Functions would be beneficial in determining the maximum height or time when an object reached its maximum height.
f(x) = -7.5x2 + 15x + 7.5 represents the path of the basketball for a floater taken by Trae Young of the Atlanta Hawks where x represents seconds the ball was in the air and y represents height of the ball in feet.
This point on the graph represents the time it took for the ball to reach its maximum height.
What is the x-value of the vertex?
The trignometric function with poor credit couldn't convince anyone to do this, resulting in being denied their loan application.
What is cosine?
Has a domain of (-∞, ∞) and a range limited by BOTH a maximum and minimum. Can model fluctuating data, sound wavelengths, & seasonal temperatures.
What are Trigonometric functions?
We could expect the function: C(x) = -2(x - 3)2 + 2 to translate this many units horiztonally.
What is 3 units to the right?
This form of Quadratic Functions would be most beneficial in determining the initial cost if tracking sales vs. cost of production.
Standard Form
f(x) = -7.5x2 + 15x + 7.5 represents the path of the basketball for a floater taken by Trae Young of the Atlanta Hawks where x represents seconds the ball was in the air and y represents height of the ball in feet.
This point on the graph represents the time it took for the ball to hit the ground.
What is the x-intercept?
A popular drink for baby parabolas.
Quadratic Formula
Domain and Range impacted by horizontal AND vertical asymptotes. Can model splitting costs within a group, ratios, and speed.
What are Rational Functions?
We could expect the -2 of the function: C(x) = -2(x - 3)2 + 2 to do this to the graph.
What is a vertical stretch?
OR
What is a reflection over the x-axis?
I can expect the function: g(x) = 3(x + 2)(x + 5) to be on this side of the y-axis.
What is the left side?
The location on the graph where we find the solutions to systems of equations.
What is the point of intersection?
Ghosts use this method to solve Quadratic Equations.
What is completing the scare?