The purpose: finding the roots of the function

Untill now we have used factorization according to the viata method in order to get the zero point of the square function.

There is an additional way to find  these points by using the formula.

The calculation will give us the amount of the zero points (2,1,0) and their values.

This formula is called " square roots formula "  the  solutions of the function are:

 ax² + bx + c =0

Click here for demonstration 

The  " square roots formula " implies that b² - 4ac which is under the square - roots, is the point which determines the number of solutions .

b²-4ac > 0 Þ    two solutions 

b²-4ac = 0 Þ     one solution   

  b²-4ac ≤ 0 Þ     no solution  

     Calculate the zero points of the following functions using the formula, 

if there is no answer put x.   

  Here are 4 functions -

        For each of  the functions answer the following questions :   

   * Find the zero points.

   * Draw a draft of graph according to the function.

   * Determine the limits in which the function is positive or negative. 

   * Determine the increasing and decreasing ranges  of the function.( hint : find the 

      vertex)

1.    y = x² +2x -15   Click here for the answer

2.    y = -2x² +x +3   Click here for the answer

3.    y = 3x ²-6x       Click here for the answer

4.    y = - x² +5x-7   Click here for the answer

Out of the " square roots formula " it seems that the expression b²-4ac, which is under

the root, is the one which determines the following.

Here are some solutions:

-two solutions      b²-4ac > 0    

-one solution        b²-4ac = 0     

-no  solution         b²-4ac ≤ 0         

think why?