Vertex Form of a Parabola

Objective: identify the vertex of a parabola using its equation; change from vertex form to standard form and standard form to vertex form.How are transformation rules used to find the vertex of a parabola? Why do we need completing the square?Vertex Form of a ParabolaStandard Form of a Quadratic

General Form of a Quadratic

StretchUp/DownLeft/RightVertexThe highest or lowest point on a parabola

Parent: f(x) = x2Vertex: (o,o)

Child: f(x) = 2(x+3)2 - 1 Vertex: _______Stretched vertically by 2, left 3, down 1Vertex Form

(h, k) is the vertexa is from the standard equationEx 1) Identify the vertex

Ex 2) Identify the vertex

Ex 3) Write the vertex form of the equation with vertex: (3, 6) a = 2Ex 4) Write the vertex form of the equation with vertex: (-8, 2) a = 3Ex 5) Find a if the vertex is (2, 5) and the graph goes through the point (4, 3)Ex 6) Find a if the vertex is (-3, 1) and the graph goes through the point (-2, 8) Changing Vertex Form to Standard Form1. Box it Out (or FOIL)

2. Distribute

3. Combined like termsEx 1) Re-write the equation in standard form

Ex 2) Re-write the equation in standard form

Changing Standard Form to Vertex From1. Move the constant term over2. Complete the Square3. Add the same about to the left side4. Factor5. Move the constant term back overEx 1) Change to vertex form

Ex 2) Change to vertex form

Ex 3) Change to vertex form