math question 2 week 7

Question

What is the quadratic formula?
What is it used for?
Provide a useful example of a quadratic equation for someone  to solve. Show your steps or at least some of your steps in how you derived to your final answer. Please do not show just the final answer 

Answer 1

The quadratic formula is a formula by which you can compute the X value of a function by using the components in its equation when Y=0, or the function crosses the x-axis. (This applies only when a does  not = 0)

 

 

The quadratic equation is as follows:

 

x= -b ± √(b² - 4ac)

                2a

 

where the function is 

ax²+bx+c = y --> ax2+bx+c = 0

 

Example:
Find the solution X to the function y= x² - 3x - 10 using the quadratic equation.

So if y=0,

 

Then:

A= 1

B= -3

C= -10

 

Therefore:

x= -(-3) ± √((-3)² - 4(1)(-10))       = 3 ± √(49)  = 3 ± 7  = 5 and -2

                        2(1)                               2                2

 

 

The solutions are -2 and 5.

This means that when y=0, or when the function crosses the x-axis, the x-values are -2 and 5.

The points at which the function crosses the x-axis are: (-2,0) and (5, 0)

:)

Answer 2

 Quadratic formula is the formula for solution of Zero's of the quadratic( i.e.) 

 

   Given a quadratic Y = ax^2 + bx + c 

 

             Roots are values of X's that make y equal 0.

 

 

        Values of X that make Y equal 0 is given by Quadratic formula of:

 

          X = - b/2a ± √(b^2 - 4ac)/2a 

 

       It is driven from factoring of aX^2 + bX + c , by completing the square. as follows

 

         a X^2 + bx + c =0

 

         a ( X^2 + b/a x +c/a ) =0

 

          we add ,and  Subtract to inside the parenthesis (b^2 /4a^2 )

 

           ( X^2 + 2 b/2a + 4b^2 /4a^2 + c/a -4b^2/ 4a^2) = 0

 

              ( X + b/2a) ^2  = 4b^2/ 4a^2 - c/a 

 

             ( X+ b/2a ) ^2 = ( b^2 - 4ac ) / 4a^2

 

                 Taking square roots of both sides:

 

               X + b/2a =± √(b^2 - 4ac) / 2a

 

 

             X = - b/2a ±√(b^2 - 4ac ) / 2a