Pre-Calculus 2.1 Quadratic Functions

Definition Quadratic Function-If f is a polynomial function and r 1 is a real number, the following statements are equivalent. – x= r 1 is a zero – x= r 1 is a solution – (x-r 1 ) is a factor – (R 1, 0) is a x-intercept Polynomial-(in one variable) an expression consisting of the sum of two or more terms each of which is the product of a constant and a variable raised to an integral power: ax 2 + bx + c is a polynomial, where a, b, and c are constants and x is a variable.

Analyzing Graphs Roots: 2, 5 Factored Form: (x-2) (x-5) Standard Form: x 2 -7x+10

Applications of Quadratics A ball is thrown from waist high at 1 meter. You throw at a speed of 18 meters per second, and it falls to the ground. A. When does the ball hit the ground and after how many seconds B. What is the maximum height C. When does the ball pass the point from which it is released

Projectile Motion Function H(x) =ax 2 + bx + c – A=the acceleration of gravity – A will either = -9.8 for meters or -16 for feet – B = initial velocity – C = initial height To find a: use the quadratic formula To find b: Use the vertex, to find the vertex, use the formula –b/2a, f(-b/2a) To find c: set function = to height of initial release, then solve for your zeros. Use the quadratic formula

Applications of Quadratics