Wilawan Srithong Nakhonsawan School Parabola Wilawan Srithong Nakhonsawan School

Contents 1 Introduction Quadratic Equation Standard Form of Parabola 2 3

What is Parabola?

What is Parabola? Ball Parabolas are the shapes that define projectile motion (the path that a ball takes when it is hit or thrown into the air).

Quadratic Equation General form: f(x) = ax2 + bx + c where a ≠ 0 ax2  Quadratic Term bx  Linear Term c  Constant Term Vertex (highest point) Vertex (lowest point) a>0: Parabola opens upward a<0: Parabola opens downward

Standard Equation f(x) = ax2 Simple form of Parabola Standard Equation The vertex of this equation is (0,0) a>0: Parabolas open upward a<0: Parabolas open upward

Standard Equation Parabola Standard Equation y = ax2  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

Example 1 Step1 Step2 Step3 Determine how the parabola opens. a, the coefficient of x2 is-2. Thus, a<0 The parabola opens downwards. Find the x-intercepts by solving Step1 Step2 Step3 Find the vertex. The vertex of the parabola is at (h,k) the parabola has its vertex at (3,8)

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)

Example 1 Step4 Step5 Find the y-intercept by computing f(0) The parabola passes through (0,-10) Step5 Graph the parabola

Example 2 Step1 Step2 Graph the quadratic function f(x)=-x2-2x+1. Use the graph identify the function’s domain and its range. Step1 Determine how the parabola opens. The coefficient of x2, is -1 (a<0)  Parabola opens downward Step2 Find the vertex. 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:

Example 2 Step3 The parabola passes through (-2.4,0) and (0.4,0) Find the x-intercepts by solving The parabola passes through (-2.4,0) and (0.4,0)

Example 2 Step4 Find the y-intercept by computing f(0) The parabola passes through (0,1)

Example 2 Step5 Graph the parabola

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