High School Mathematics - Functions and Equations

Zero function

• In general, if the function y = f (x) at the value of the real number a is equal to 0, then this function is called a  zero

Discriminant

• For quadratic function, Y = AX ² + BX + C
• When B = [Delta] ² - when 4ac> 0, the equation AX ² + BX + C = 0 has two real roots are not equal, then the quadratic function AX = Y ² + BX + C has two zeros
• When B = [Delta] ² - 4ac = 0, the equation AX ² + BX + C = 0 has two real roots are not equal, then the quadratic function AX = Y ² + BX + C has a double zero
• When B = [Delta] ² - 4ac <0, equation AX ² + BX + C = 0 has two real roots are not equal, then the quadratic function AX = Y ² + BX + C is not zero

Properties of quadratic function of the image

• Image quadratic function is continuous, as it passes through zero, the function changes sign
• Two adjacent zeros of all the functions between the value remains the same number

The method of calculating approximate solutions seek function zero - dichotomy

1. D taken in a closed interval [a, b] ⊆D, so that f (a) and f (b) of opposite sign, i.e., f (a) ^. F (b) <0, so that a0 = a, b0 = b
2. Take midpoint interval [a0, b0] is, x0 = a0 + 1/2 (b0 - a0) = 1/2 (a0 + b0), calculates f (x0) and f (a0)
3. Calculating boundary value, if the presence of 0, the calculated zero, otherwise repeat the above steps