QUADRATIC EQUATIONS in VERTEX FORM y = a(b(x – h)) 2 + k.

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Presentation transcript:

QUADRATIC EQUATIONS in VERTEX FORM y = a(b(x – h)) 2 + k

y = a(b(x – h)) 2 + k h: move LEFT or RIGHT k: move UP or DOWN a: opens UP or DOWN opens WIDE or NARROW b: compresses or stretches in x-direction

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

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

Move UP when y = x 2 + k or Move DOWN when y = x 2 – k this is called a vertical shift

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

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? The parabola opens down and moves up 8.

What happens? The parabola moves left 8.

What happens? The parabola opens wider and moves up 3.

What happens? The parabola moves right 4 and moves up 2

The parabola opens down, moves right 3 and moves up 4. What happens?

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.

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

Write an equation The graph has moved right 3 and moved up 5.

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