Unit 7 Quadratics Graphing Quadratic Functions Goal: I can graph quadratic functions in Factored Form and show intercepts, maxima and minima. (F-IF.8a)
Graphing a Quadratic Function in Factored Form Step 1 Multiply Step 2 Find Step 3 Make Step 4 Plot to write in standard/function form y = ax²+bx+c the x-coordinate of the vertex, which is a table of values, using x-values to the left and right of the vertex the points and connect them with a smooth curve to form a parabola
EXAMPLE 1 1. Standard Form: 2. Find the x and y-coordinate of the vertex: y -coordinate y = (3)2 – 6(3) + 5 y = 9 – 6(3) + 5 y = 9 – 18+ 5 y = – 4 vertex: (3, -4)
EXAMPLE 1 Fill in the table of values to graph the quadratic. 3. Make a table of values: X Y vtx 1 y = (1)2 – 6(1) + 5 2 -3 y = (2)2 – 6(2) + 5 3 -4 y = (4)2 – 6(4) + 5 4 -3 5 y = (5)2 – 6(5) + 5
EXAMPLE 1 Graph Quadratic Function 4. Plot: X Y vtx 1 2 -3 3 -4 4 -3 5
EXAMPLE 2 1. Standard Form: 2. Find the x-coordinate of the vertex: y -coordinate y =-2 (0)2 + 6 y =-2 (0) + 6 y = (0) + 6 y = 6 vertex: (0, 6)
EXAMPLE 2 Fill in the table of values to graph the quadratic. 3. Make a table of values: X Y vtx y = -2(-2)2 + 6 -2 -2 -1 4 y = -2(-1)2 + 6 y = -2(1)2 + 6 6 1 4 y = -2(2)2 + 6 2 -2