Parabola Wilawan Srithong Nakhonsawan School Contents 2 1

Parabola Wilawan Srithong Nakhonsawan School

Contents 2 1 Introduction 2 Quadratic Equation 3 Standard Form of Parabola

What is Parabola? 3

What is Parabola? Ball 4

Quadratic Equation General form: f)x( = ax 2 + bx + c ax 2 Quadratic Term bx Linear Term c Constant Term where a ≠ 0 Vertex (highest point) Vertex (lowest point) a>0: Parabola opens upward 5 a<0: Parabola opens downward

Standard Equation Simple form of Parabola Standard Equation f)x( = ax 2 The vertex of this equation is (0, 0) a>0: Parabolas open upward 6 a<0: Parabolas open upward

Standard Equation Parabola Standard Equation y = ax 2 7 y = a(x-h)2 + k

Example 1 Graph the quadratic function We begin by identifying values for a, h, and k Standard form a=-2 h=3 k=8 Given function 8

Example 1 Step 1 Determine how the parabola opens. a, the coefficient of x 2 is-2. Thus, a<0 The parabola opens downwards. 9 Step 2 Find the vertex. The vertex of the parabola is at )h, k( the parabola has its vertex at )3, 8( Step 3 Find the xintercepts by solving

Example 1 Step 3 Find the x-intercepts by solving The x-intercepts are 1 and 5. The parabola passes through )1, 0( and )5, 0( 10

Example 1 Step 4 Find the y-intercept by computing f)0 ( The parabola passes through )0, -10( Step 5 11 Graph the parabola

Example 2 Graph the quadratic function f)x(=-x 2 -2 x+1. Use the graph identify the function’s domain and its range. Step 1 Determine how the parabola opens. The coefficient of x 2, is -1 )a<0 ( Parabola opens downward Find the vertex. Step 2 12 The x-coordinate of the vertex is We identify a, b, and c in

Example 2 Substitute -1 for a and -2 for b into the equation for the x-coordinate : The x-coordinate of the vertex is -1 and the vertex is at )-1, f)-1(( We substitute -1 for x in the equation of the function, to find the y-coordinate: 13

Example 2 Step 3 Find the x-intercepts by solving The parabola passes through )-2. 4, 0 (and )0. 4, 0( 14

Example 2 Step 4 Find the y-intercept by computing f)0 ( The parabola passes through )0, 1( 15

Example 2 Step 5 16 Graph the parabola