Vertex Form of a Parabola

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Presentation transcript:

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”?

Standard Form of a Quadratic

General Form of a Quadratic Stretch Up/Down Left/Right

Vertex The highest or lowest point on a parabola

Parent: f(x) = x2 Vertex: (o,o)

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

“a” is from the standard equation Vertex Form (h, k) is the vertex “a” is from the standard equation

Ex 1) Identify the vertex

Ex 2) Identify the vertex

Ex 3) Write the vertex form of the equation with vertex: (3, 6) a = 2

Ex 4) Write the vertex form of the equation with vertex: (-8, 2) a = 3

Ex 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 Form 1. Box it Out (or FOIL) 2. Distribute 3. Combined like terms

Ex 1) Re-write the equation in standard form

Ex 2) Re-write the equation in standard form

Changing Standard Form to Vertex From 1. Move the constant term over 2. Complete the Square 3. Add the same about to the left side 4. Factor 5. Move the constant term back over

Ex 1) Change to vertex form

Ex 2) Change to vertex form

Ex 3) Change to vertex form