Graphing Quadratics Questions to consider: 1. What are some points of interest that we can use when graphing quadratics? 2. What are the different forms of a quadratic and what pieces of information do they give us? What is the y value of any point on the x-axis? What is the x value of any point on the y-axis? This means, if we want to find the x-intercepts, then we should set y=0. If we want to find the y-intercepts, then we should set x=0. There are three forms of a quadratic that we are going to talk about: 1. Standard Form: 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 −𝑏 The x-value of the vertex is Axis of symmetry is 𝑥 = This is easily factorable −𝑏 2𝑎 2𝑎 2. Vertex Form: 𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘 vertex is (h, k) – remember bad dog axis of symmetry is 𝑥 = ℎ 3. Intercept Form: 𝑎(𝑥 − 𝑝)(𝑥 − 𝑞) x-intercepts are 𝑝 and 𝑞 axis is halfway between 𝑝 and 𝑞 In any form, if 𝑎 > 0, then the graph opens ______________ If 𝑎 < 0, then the graph opens ___________ The graph gets ________________ as |𝑎| gets larger. The graph gets ________________ as |𝑎| gets smaller. Some good starting points 𝑏 vertex – probably using − 2𝑎 does it open up or down? x-intercepts y-intercepts May need to plug in some points – the good ol’ table method Lets try some: 𝑦 = 2𝑥 2 − 8𝑥 + 6 Vertex x-int y-int Up/down? You try one: 𝑦 = 𝑥 2 − 𝑥 − 12 Vertex x-int y-int Up/down? Let’s try one in vertex form: 1 𝑦 = − (𝑥 + 3)2 + 4 2 Vertex y-int Up/down? Your turn: 𝑦 = 2(𝑥 − 1)2 + 3 Vertex y-int Up/down? In intercept form: 𝑦 = −(𝑥 + 2)(𝑥 − 4) x-int y-int Up/down? Vertex Putting equations in standard form: just simplify!! a.) 𝑦 = −(𝑥 + 4)(𝑥 − 9) b.) 3(𝑥 − 1)2 + 8