Quadratic+Equations

__Standard Form__: Y = ax ^2 + bx + c
The point the graph touches the axis on the X is called the __//**line of symmetry**//__. The point where the line touches one of the axis is called the __**//Vertex//**__. __**//Maximum//**__ Is When //**A**// is less than is less than **//Zero.//** __//**Minimum**//__ Is when **//A//** is greater than **//Zero//**.



Up here to the right the vertex is a minimum. a > 0

-**__Axis of Symmetry-__** X= (-b/2a) Ex: Find the axis of Symmetry and the Vertex point 1. Y= x^2 - 10x + 2 X = __-(-10)__ = __10__ = 5 2(1) 2

Y = (5)^2 - 10(5) + 2 Y = 25 - 50 + 2 Y = -24
 * Vertex: ( 5, -24)**

Y = 3x^2 + 18x + 9 X = __-b__ = __-18__ = __-18__ = -3 2a 2(3) 6 Y = 3(-3)^2 + 18(-3) + 9 Y = 27 - 54 + 9 Y = 18
 * Vertex: ( -3, 18) Minimum**

I. Graphing Quadratics Y = ax^2 + bx + 5 y = -3x^2 + 6x + 5 Step 1: Axis of symmetry x = __-b__ = __-6__ = __-6__ = **1** 2(a) 2(-3) -6

Step 2: Find The vertex Y = -3(1)^2 + 6(1) + 5 Y = -3 + 6 + 5 (1,8)**
 * Y = 8

Step 3: Find the other Points ( Y- intercept) Y = -3(0)^2 + 6(0) + 5
 * Y = 5**

I. Solve By Graphing Roots: Where the Parabola Crosses the X - axis This is a graph with no roots. This graph has only one root.

This graph has two roots. Ex: Solve By Graphing and Finding the Roots 1. Y = x^2 - 4 A. X = __-0__ = 0 2(1) B. Vertex: Y = 0^2 - 4 (0,-4) C. X - intercept 0 = X^2 - 4 4 = X^2
 * X = + or - 2**

2. Y = X^2 A. Axis: X = 0 B. Vertex: Y = 0^2 C. X - Intecept: Y = (0,0) X^2 = 0
 * X = 0**

Quadratic Word Problems: Find a positive number(s) whose square is less than 15 times the number. X: number X^2 = 15X - 36 X^2 - 15X + 36m = 0 (X + 12) (X + 3) X = 3
 * X = 12

Sites for more information: http://www.purplemath.com/modules/grphquad2.htm http://library.thinkquest.org/29292/quadratic/4graphing/index.htm**