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math question 2 week 7

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2 Answers

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= x- 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)

:)
 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/2+ 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