QUADRATIC EQUATIONSin

VERTEX FORMy = a(b(x – h))2 + k

y = a(b(x – h))2 + k

h: move LEFT or RIGHTk: move UP or DOWNa: opens UP or DOWN opens WIDE or NARROWb: compresses or stretches in x-direction

2y x2 2y x

Notice the parabola moved up 2 along the y-axis.

2y x2 2y x

Notice the parabola moved down 2 along the y-axis.

Move UP when y = x2 + kor

Move DOWN when y = x2 – k

this is called a

vertical shift

2y x 2( 2) y x

Notice the parabola moved right 2 along the x-axis.

2y x 2( 2) y x

Notice the parabola moved left 2 along the x-axis.

Move LEFT when y = (x + h)2

or

Move RIGHT when y = (x – h)2

this is called a

horizontal shift

Graph opens UP if a is positive as Graph opens DOWN if a is negative

y = a(x – h)2 + k

What happens?

2 8 y xThe parabola opens down and moves up 8.

What happens?

2( 8) y xThe parabola moves left 8.

What happens?

212 3 y x

The parabola opens wider and moves up 3.

2( 4) 2 y x

What happens?

The parabola moves right 4 and moves up 2

25( 3) 4 y xThe parabola opens down, moves right 3 and moves up 4.

What happens?

214 ( 2) 3 y x

The parabola opens down, becomes wider, moves left 2, and moves down 3.

What happens?

Write an equation

The graph has moved up 6 along the y-axis.

2 6 y x

Write an equation

The graph has moved left 3 along the x-axis.

2( 3) y x

Write an equation

The graph has moved right 3 and moved up 5.

2( 3) 5 y x

Write an equation

The graph opens down, moves left 6 and moves up 2.

2( 6) 2 y x