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# math question 2 week 7

What is it used for?

### 2 Answers by Expert Tutors

Stephanie T. | Stephanie, Education ExtraordinaireStephanie, Education Extraordinaire
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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)

:)
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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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