Standard form of quadratic function

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1. Standard Form of Quadratic Function

2. 2   The expression  a x 2  + b x + c ( quadratic function in one variable )  in the definition of a quadratic function is a polynomial of   degree of 2   or  second order , or a  2nd degree polynomial , since the highest exponent of x is 2. This expression is called  quadratic polynomial   or   quadratic . If the quadratic is set equal to zero, then the result is a   quadratic equation  or a  second degree equation . The general form of the quadratic equation is  ax 2  + bx + c = 0 , where a, b, and c are constants and a ≠ 0.

3. 3 Writing quadratic equation in standard form / general form The general form of the quadratic equation is  ax 2  + bx + c = 0 , where a, b, and c are constants and a ≠ 0 . Example 1. Write x 2 = 2x + 2 in standard form . x 2 – 2x – 2 = 0 (standard form) a = 1, b = -2, c = -2

4. 4 Example 2. Write 2x – x 2 + 9 = 0 in standard form. Example 3. Write x 2 = 9 in standard form. ax 2  + bx + c = 0 -x 2 + 2x + 9 = (since the value of a is negative, divide or multiply both sides by -1) = x 2 – 2x – 9 = 0 a = 1, b = -2, c = -9 ax 2  + bx + c = 0 x 2 – 9 = 0 a = 1, b = 0, c = -9 Example 2. Write 2x – x 2 + 9 = 0 in standard form. Example 3. Write x 2 = 9 in standard form. ax 2  + bx + c = 0 x 2 – 9 = 0 a = 1, b = 0, c = -9