E XAMPLE 1 Graph = 2 2 + 1 The vertex is (2, 1). Since the x- - PowerPoint PPT Presentation

D AY 127 – G RAPHING Q UADRATICS

G RAPHING P ARABOLAS IN V ERTEX F ORM 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.

E XAMPLE 1 Graph 𝑔 𝑦 = 𝑦 − 2 2 + 1 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). x f(x) 0 5 1 2 Then , plug in 0, 1, 3, 4 for “x” Vertex! 2 1 and see what we get for f(x). 3 2 4 5

G RAPHING Q UADRATIC E QUATION IN I NTERCEPT F ORM  Another way to graph quadratics.  Intercept form of a quadratic is its factored form  Example: Intercept form of 𝑔 𝑦 = 𝑦 2 − 10𝑦 + 21 is 𝑔 𝑦 = (𝑦 − 7)(𝑦 − 3)

G ENERAL R ULES FOR G RAPHING Q UADRATICS OF THE F ORM 𝑔 𝑦 = 𝑏(𝑦 − 𝑞)(𝑦 − 𝑟) 1) Identify the x-intercept and plot them • x-intercepts for 𝑔 𝑦 = 𝑏 𝑦 − 𝑞 𝑦 − 𝑟 are (𝑞, 0) and 𝑟, 0 2) Find the vertex and axis of symmetry 𝑞+𝑟 • the x-coordinate of the vertex is 𝑦 = 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 𝑞+𝑟 • Axis of symmetry is 𝑦 = 2

G ENERAL R ULES FOR G RAPHING Q UADRATICS OF THE F ORM 𝑔 𝑦 = 𝑏(𝑦 − 𝑞)(𝑦 − 𝑟) 3) Find the y-intercept; reflect over axis of symmetry • calculate 𝑔(0) to find the y-intercept 4) Find one or two other points if needed, reflecting over axis of symmetry 5) Sketch curve

G ENERAL R ULES FOR G RAPHING Q UADRATICS OF THE F ORM 𝑔 𝑦 = 𝑏(𝑦 − 𝑞)(𝑦 − 𝑟) Example: Graph 𝒈 𝒚 = 𝒚 − 𝟖 𝒚 − 𝟒 1) Identify the x-intercepts and plot them • x-intercepts are (7, 0) and (3, 0) 2) Find the vertex and axis of symmetry 𝑞+𝑟 𝑦 = 2 = 5; 𝑔 5 = −4 • • Axis of symmetry is 𝑦 = 5 3) Find the y-intercept; reflect over axis of symmetry • y-int = 𝑔 0 = 21

G ENERAL R ULES FOR G RAPHING Q UADRATICS OF THE F ORM 𝑔 𝑦 = 𝑏(𝑦 − 𝑞)(𝑦 − 𝑟) 4) Find one or two other points if needed, reflecting over axis of symmetry 5) Sketch curve