FUNCTIONS MATHS

FUNCTIONS MATHS

1. QUADRATIC FUNCTIONS

   • It is a polynomial function with one or more variables in which the highest degree term is second
     • should consider
       • Perfect square trinomial
         • Example:
           • x² + 10x + 25 = (x + 5)²
       • Difference of squares
         • Example:
           • 16x² -25y² = (4x – 5y) (4x + 5y)
   • Its graphic representation is a vertical parabola.
     • The formula for calculating a quadratic equation is:
       • • Example:
           • A shot putter can be modeled using the equation, y = 0.0241 x² + x + 5.5. Where x is the distance traveled (in feet) and y y is the height (also in feet). How long is the shot?
             • Answer: The shot is about 46.41 feet

2. EXPONENTIAL FUNCTIONS

   • It is the one that the independent variable x appears in the exponent and has a constant a as its base. Its expression is:
     • F(x) = a^x
       • All exponential functions exp (x) have the following properties:
         • Example:
           • (8^4 )^3= 8^(4*3) = 6.87
           • 9^2 . 9^4 = 9^(2+4)= 531441
           • 9²/9³ = 9^(2-3) = 0.11
           • (18/5)^(-1)= 5/18
           • (24)^0 = 1

3. TRIGONOMETRIC FUNCTIONS

   • • With the legs being the "a" and "b" sides, and the hypotenuse being the major side "c"
       • • It must be taken into account that if you change the angle, then the legs change: the opposite becomes the contiguous.
   • Example:
     • The hypotenuse measures, 11,3
     • Cities A, B and C are the vertices of a right triangle. Calculate the distance between cities A and C and between cities B and C if city B is 100km from city A and the road that A with B forms an angle of 35º with the road that connects A to C.
       • Therefore, the distance between cities A and C is 122.1 kilometers and the distance between cities B and C is 70.08 km.

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