quadratic equations in vertex form y = a(b(x – h)) 2 + k
TRANSCRIPT
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QUADRATIC EQUATIONSin
VERTEX FORMy = a(b(x – h))2 + k
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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
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2y x2 2y x
Notice the parabola moved up 2 along the y-axis.
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2y x2 2y x
Notice the parabola moved down 2 along the y-axis.
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Move UP when y = x2 + kor
Move DOWN when y = x2 – k
this is called a
vertical shift
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2y x 2( 2) y x
Notice the parabola moved right 2 along the x-axis.
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2y x 2( 2) y x
Notice the parabola moved left 2 along the x-axis.
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Move LEFT when y = (x + h)2
or
Move RIGHT when y = (x – h)2
this is called a
horizontal shift
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Graph opens UP if a is positive as Graph opens DOWN if a is negative
y = a(x – h)2 + k
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What happens?
2 8 y xThe parabola opens down and moves up 8.
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What happens?
2( 8) y xThe parabola moves left 8.
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What happens?
212 3 y x
The parabola opens wider and moves up 3.
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2( 4) 2 y x
What happens?
The parabola moves right 4 and moves up 2
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25( 3) 4 y xThe parabola opens down, moves right 3 and moves up 4.
What happens?
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214 ( 2) 3 y x
The parabola opens down, becomes wider, moves left 2, and moves down 3.
What happens?
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Write an equation
The graph has moved up 6 along the y-axis.
2 6 y x
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Write an equation
The graph has moved left 3 along the x-axis.
2( 3) y x
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Write an equation
The graph has moved right 3 and moved up 5.
2( 3) 5 y x
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Write an equation
The graph opens down, moves left 6 and moves up 2.
2( 6) 2 y x