# Math/Elective Algebra

Topics: Quadratic equation, Elementary algebra, Completing the square Pages: 2 (263 words) Published: January 28, 2011

ax2 + bx + c = 0

1. x2 +2x – 8 = 0
2. x2 – 10x + 25 = 0
3. 3x2 + x - 2 = 0

If [pic] a x2 + b x + c = 0, then [pic]

Finding the zeros of the quadratic functions

- The zeros of a function are the input values which result in an output value of zero.

One way of solving quadratic equations is using factoring
Examples are the following:
1) x2 + 5x + 6 = 0
Set this equal to zero:
(x + 2)(x + 3) = 0
x + 2 = 0 or x + 3 = 0
x = –2 or x = – 3
Then, clearly, the zeros are -2 and -3, since those are the input values which will result in an output value of zero.

2) x(x + 5) = 03) x2 – 4 = 0
x = 0 or x + 5 = 0  (x – 2) (x + 2) = 0
x = 0 or x = –5x – 2 = 0 or x + 2 = 0
x = 2 or x = –2

Given, f ( x ) = 2 x2 + 8 x + 1, the zeros are the values of x which result in an output value of y = 0.  Thus the zeros are the solutions of the equation
2 x2 + 8 x + 1 = 0

Using the quadratic formula, we get

[pic]

Another way of solving quadratic equations is using completing the square

x2 + 6x – 7 = 0
x2 + 6x = 7
x2 + 6x + 9 = 7 + 9
(x+3)2 = 16
x + 4 = ± 4
x = – 3 ± 4
= – 3 – 4, –3 + 4
= –7, +1