Determine the number of solutions of a quadratic equation

The  exercise appears under the Algebra I Math Mission. This exercise practices analyzing quadratic equations in order to determine how many different real number solutions they have.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the discriminant and the number of solutions of $$f(x)$$: This problem provides the value of the function $$f(x)$$. The student is asked to figure out the discriminant and number of solutions for $$f(x)$$. Stqe1.png

Strategies
Knowledge of the quadratic formula and strength in arithmetic are encouraged to ensure success on this exercise.
 * 1) When the discriminant $$ D=b^2-4ac$$ is negative the quadratic formula will yield imaginary solutions.
 * 2) The sign of the discriminant tells us what kind of roots a quadratic function has:
 * 3) A negative discriminant indicates that neither of the roots are real numbers.
 * 4) A discriminant of zero indicates that the function has a repeated real number root.
 * 5) A positive discriminant indicates that the function has two distinct real number roots.

Real-life Applications

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