Transforming Quadratic Functions in Standard Form

1

How can I re-write a quadratic function in standard form?

1.1

2

y = 2(x − 5) − 3 2

How can I re-write a quadratic function in standard form?

2

y = 2(x − 5) − 3 2.1

2

y = 2(x − 5) − 3

Vertex, Mimimum

3

2

y = 2(x − 5) − 3

vertex form

4

2

y = 2(x − 5) − 3 2

y = a(x − h) + k

vertex form 5

2

y = 2(x − 5) − 3 2

y = a(x − h) + k vertex form

a 6

2

y = 2(x − 5) − 3 2

y = a(x − h) + k vertex form

a

is the coefficient of the quadratic term, which determines whether the parabola opens up or down.

7

2

y = 2(x − 5) − 3 2

y = a(x − h) + k

a

is the coefficient of the quadratic term, which determines whether the parabola opens up or down.

(h, k) 8

2

y = 2(x − 5) − 3 2

y = a(x − h) + k

a

is the coefficient of the quadratic term, which determines whether the parabola opens up or down.

(h, k)

is the vertex of the parabola 9

2

y = 2(x − 5) − 3 2

y = a(x − h) + k

(h, k) 2

y = ax + bx + c 10

2

y = 2(x − 5) − 3

2

y = ax + bx + c 11

2

y = 2(x − 5) − 3 We can expand the square using the identity

2

y = ax + bx + c 12

2

y = 2(x − 5) − 3 2

2

2

a − 2ab + b = (a − b)

2

y = ax + bx + c 13

2

y = 2(x − 5) − 3 2

2

2

a − 2ab + b = (a − b) 2

y = 2(x − 10x + 25) − 3 2

y = ax + bx + c 14

2

y = 2(x − 5) − 3 2

2

2

a − 2ab + b = (a − b) 2 y = 2(x − 10x + 25) − 3 2

y = 2x − 20x + 47 15

2

y = 2(x − 5) − 3 2

2

2

a − 2ab + b = (a − b) 2 y = 2(x − 10x + 25) − 3 2

y = 2x − 20x + 47 2

y = ax + bx + c 16