2 CLASSIFYING EQUATIONS y = 2x²+ 7x + 3y = 2x + 4What is the pattern ?y = 5x²y = 5xy = x² - 4y = x - 4LINEARQUADRATIC
3 Standard Form of a Quadratic Equation y = ax²+ bx + c (a ≠ 0)An equation is called QUADRATIC ifit has a squared variableThere MUST be a squared variable.There may or may not be the “middle term”or the constant.
4 Every quadratic function has a U-shaped graph called a parabola. vertex●●vertexThe vertex of a parabola is the lowest point of a parabola that opens up and the highest point of a parabola that opens down.
5 The axis of symmetry of a parabola is the line passing through the vertex that divides the parabola into two symmetric parts.vertex●●vertexaxis of symmetryaxis of symmetry
6 Identifying a, b and c y = ax²+ bx + c (a ≠ 0) In y = 2x²+ 3x – 5 a = -5In y = -x²- 5x + 2a =-1b =-5c =2In y = x²- 3xa =1b =-3c =In y = -x²+ 4a =-1b =c =4In y = -3x²a =-3b =c =
7 The effect of a on the parabola y = x²+ 2x + 1y = -x²+ 2x + 1a = 1a = -1If a is positivethe parabola opens upIf a is negativethe parabola opens down
8 Finding the vertex In the equation y = ax²+ bx + c ●In the equation y = ax²+ bx + cthe x coordinate of the vertexcan be found using the formula:Then substitute the x value into the original equation to find the y coordinateIn y = x²+ 4x + 8a =1b =4c =8y = (-2)² + 4(-2) + 8VERTEX: x =y = = 4VERTEX: (-2, 4)
9 Graphing a Quadratic Function STEPSFind the x coordinate of the vertex:Draw the line of symmetry at the x-value.Then substitute the x value to find y.The vertex will be an ordered pair (x,y).x =Make an x/y table. Choose x values to the left and right of the vertex. Plot as you go.Connect the points as a smooth curve.
10 x y Graph: y = x²- 2x - 3 = = 1 Vertex: x = y = (1)² - 2(1) – 3 = -4 -1●●x-31-4●●2-3●3
11 x y Graph: y = -x²+ 2x - 3 = = 1 Vertex: x = y = -(1)² + 2(1) – 3 = -2 ●-1-6●●x-31-22-3●●3-6
12 A Few together from the Homework pg # 5 and #15