4.2 Graph Quadratic Functions in Vertex or Intercept Form

To graph quadratic functions in vertex or intercept form To write equations in standard form

Vertex Form y  a(x h) 2  k + + Characteristics: The vertex is (h, k) The axis of symmetry is x = h a controls the width of the graph and if opens up or down

Graph y = -2(x-3) 2 +4 Vertex: (3, 4) Fill out a chart. Remember, you pick the x value and solve for y.

x y 2 2 1 0 -4 -14

Intercept Form y  a(x p)(x q)

Graph y = 2(x + 3)(x – 1) Steps: 1.Plot x intercepts 2. Find axis of symmetry 3. Find the coordinates of vertex 4. Plot some pts 5. Connect the dots 1. What makes y = 0?...-3 & 1 2. -3+1 = 2 then divide in ½ = -1 3. Plug -1 into equation for x and solve for y.

4. Find more pts Pick x and solve for y.

To Standard Form Goal: Make the equations look like ax 2 + bx + c Example: Write f(x) = 4(x-2) 2 +1 in standard form = 4(x - 2)(x - 2) + 1 = 4(x 2 – 4x + 4) +1 = 4x 2 – 16x + 16 + 1 = 4x 2 – 16x + 17

Homework: Pg 249 1 – 37 Every other odd, 53