Presentation on theme: "3.2 Graphing Quadratic Functions in Vertex or Intercept Form"— Presentation transcript:
13.2 Graphing Quadratic Functions in Vertex or Intercept Form Definitions3 FormsGraphing in vertex formExamplesChanging between eqn. forms
2Quadratic FunctionA function of the form y=ax2+bx+c where a≠0 making a u-shaped graph called a parabola.Example quadratic equation:
3Vertex- Axis of symmetry- The lowest or highest point of a parabola. The vertical line through the vertex of the parabola.Axis ofSymmetry
4Vertex Form Equation y=a(x-h)2+k If a is positive, parabola opens up If a is negative, parabola opens down.The vertex is the point (h,k).The axis of symmetry is the vertical line x=h.
5Vertex Form (x – h)2 + k – vertex form Each function we just looked at can be written in the form (x – h)2 + k, where (h , k) is the vertex of the parabola, and x = h is its axis of symmetry.(x – h)2 + k – vertex formEquationVertexAxis of Symmetryy = x2 or y = (x – 0)2 + 0(0 , 0)x = 0y = x2 + 2 or y = (x – 0)2 + 2(0 , 2)y = (x – 3)2 or y = (x – 3)2 + 0(3 , 0)x = 3
6Analyze y = (x + 2)2 + 1. Example 1: Graph Step 1 Plot the vertex (-2 , 1)Step 2 Draw the axis of symmetry, x = -2.Step 3 Find and plot two points on one side , such as (-1, 2) and (0 , 5).Step 4 Use symmetry to complete the graph, or find two points onthe left side of the vertex.
7Your Turn!Analyze and Graph:y = (x + 4)2 - 3.(-4,-3)
8Example 2: Graph y=-.5(x+3)2+4 a is negative (a = -.5), so parabola opens down.Vertex is (h,k) or (-3,4)Axis of symmetry is the vertical line x = -3Table of values x y-1 2-3 4-5 2Vertex (-3,4)(-4,3.5)(-2,3.5)(-5,2)(-1,2)x=-3
9Table of values with 5 points? Now you try one!y=2(x-1)2+3Open up or down?Vertex?Axis of symmetry?Table of values with 5 points?
11Changing from vertex or intercepts form to standard form The key is to follow ORDER OF OPERATIONSEx: y=-(x+4)(x-9) Ex: y=3(x-1)2+8=-(x2-9x+4x-36) =3(x-1)(x-1)+8=-(x2-5x-36) =3(x2-x-x+1)+8y=-x2+5x =3(x2-2x+1)+8=3x2-6x+3+8y=3x2-6x+11
12Changing from vertex or intercepts form to standard form Practice:1: y = 3(x-4)(x+2)2: y = -2(x-3)2 - 5
13Challenge ProblemWrite the equation of the graph in vertex form.