Compare properties of quadratic functions

The  exercise appears under the Algebra I Math Mission. This exercise practices comparing the properties of two quadratic functions, each represented in a different way.

Types of Problems
There are three types of problems in this exercise:


 * 1) Find the function that has a greater x or y-intercept: This problem provides the value of the function $$f(x)$$ with a graph of the function. The student is asked to compare it to the other functions and determine the function that has a greater x or y-intercept. Compare properties of quadratic functions.PNG
 * 2) Find how many roots the functions have in common: This problem provides the value of the function $$f(x)$$ with a graph of the function. The student is asked to compare it to the other functions and determine the number of roots the functions has in common.Compare properties of quadratic functions2.PNG
 * 3) Find the function that has a greater minimum or maximum: This problem provides the value of the function $$f(x)$$ with a graph of the function. The student is asked to compare it to the other functions and determine the function that has a greater minimum or maximum. Compare properties of quadratic functions3.PNG

Strategies
Knowledge of the quadratic formula and strength in arithmetic are encouraged to ensure success on this exercise.
 * 1) The y-intercept of a function is the value at which it crosses the y-axis. At this value, $$x=0x$$
 * 2) When a function is presented as a formula, students can simply evaluate it at $$x=0$$.
 * 3) When a function is presented as a graph, students should look for the y-coordinate of the intersection point of the graph with the y-axis.
 * 4) The roots, or x-intercepts, of a function are the values at which the function crosses the x-axis. At these values, the function equals 0.
 * 5) When a function is presented as a formula, students can find its roots by setting it equal to 0 and solving the resulting equation.
 * 6) When a function is presented as a graph, students should look for the x-coordinates of the intersection points of the graph with the x-axis.

Real-life Applications

 * 1) Quadratics are used to model acceleration due to gravity and are useful in the inverse square law from physics.