Day 127 – Graphing Quadratics

Graphing Parabolas in Vertex Form Remember, when we’re graphing a parabola, we want to find the vertex first, and then find two other points on either side of the vertex to the graph so that we get the curved shape we’re all familiar with. When a quadratic equation is in vertex form, the vertex is much easier to find than if the quadratic equation is in standard form.

Example 1 Graph 𝑓 𝑥 = 𝑥−2 2 +1 Then, plug in 0, 1, 3, 4 for “x” The vertex is (2, 1). Since the x- values for the vertex is “2”. Then for the other x-values, we’ll pick 3 and 4 on the left and 0 and 1 on the right. (The two nearest, nice x-vales to x = 2). Then, plug in 0, 1, 3, 4 for “x” and see what we get for f(x). x f(x) 5 1 2 3 4 Vertex!

Graphing Quadratic Equation in Intercept Form Another way to graph quadratics. Intercept form of a quadratic is its factored form Example: Intercept form of 𝑓 𝑥 = 𝑥 2 −10𝑥+21 is 𝑓 𝑥 =(𝑥−7)(𝑥−3)

General Rules for Graphing Quadratics of the Form 𝑓 𝑥 =𝑎(𝑥−𝑝)(𝑥−𝑞) 1) Identify the x-intercept and plot them x-intercepts for 𝑓 𝑥 =𝑎 𝑥−𝑝 𝑥−𝑞 are (𝑝, 0) and 𝑞, 0 2) Find the vertex and axis of symmetry the x-coordinate of the vertex is 𝑥= 𝑝+𝑞 2 (think about it – it’s located halfway between the zeros) plug in the x-coordinate of the vertex to find its y- coordinate; plot point Axis of symmetry is 𝑥= 𝑝+𝑞 2

General Rules for Graphing Quadratics of the Form 𝑓 𝑥 =𝑎(𝑥−𝑝)(𝑥−𝑞) 3) Find the y-intercept; reflect over axis of symmetry calculate 𝑓(0) to find the y-intercept 4) Find one or two other points if needed, reflecting over axis of symmetry 5) Sketch curve

General Rules for Graphing Quadratics of the Form 𝑓 𝑥 =𝑎(𝑥−𝑝)(𝑥−𝑞) Example: Graph 𝒇 𝒙 = 𝒙−𝟕 𝒙−𝟑 1) Identify the x-intercepts and plot them x-intercepts are (7, 0) and (3, 0) 2) Find the vertex and axis of symmetry 𝑥= 𝑝+𝑞 2 =5;𝑓 5 =−4 Axis of symmetry is 𝑥=5 3) Find the y-intercept; reflect over axis of symmetry y-int = 𝑓 0 =21

General Rules for Graphing Quadratics of the Form 𝑓 𝑥 =𝑎(𝑥−𝑝)(𝑥−𝑞) 4) Find one or two other points if needed, reflecting over axis of symmetry 5) Sketch curve