2012-02-22 Transition to Vertex Form

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Algebra II | Packer Collegiate Institute A Transition to Vertex Form (1) You know (2, −3) is the vertex of a parabola of the form y = x 2 + bx + c . Graph the parabola.

(2) You know (−6, 7) is the vertex of a parabola of the form y = − x 2 + bx + c . Graph the parabola.

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Understanding the Vertex (3) What is the minimum value that y can be, in the equation y = x 2 ? What is the x value that corresponds with that minimum y value? Explain your reasoning.

(4) What is the minimum value that y can be, in the equation y = x 2 + 2 ? What is the x value that corresponds with that minimum y value? Explain your reasoning.

(5) What is the minimum value that y can be, in the equation y = x 2 − 5 ? What is the x value that corresponds with that minimum y value? Explain your reasoning.

(6) What is the minimum value that y can be, in the equation y = ( x − 2) 2 ? What is the x value that corresponds with that minimum y value? Explain your reasoning.

(7) What is the minimum value that y can be, in the equation y = ( x − 2) 2 − 3 ? What is the x value that corresponds with that minimum y value? Explain your reasoning.

(8) What is the maximum value that y can be, in the equation y = −( x + 1) 2 ? What is the x value that corresponds with that maximum y value? Explain your reasoning.

(9) What is the maximum value that y can be, in the equation y = −( x + 1) 2 + 3 ? What is the x value that corresponds with that maximum y value? Explain your reasoning.

(10) For each equation, answer what the vertex of the parabola is, and whether the parabola opens upwards or downwards. 2

(a) y = x 2

(b) y = ( x − 3) 2 + 4

vertex:

vertex:

circle one: opens upwards / downwards

circle one: opens upwards / downwards

(c) y = −( x − 3) 2 + 4

(d) y = ( x + 2) 2 − 1

vertex:

vertex:

circle one: opens upwards / downwards

circle one: opens upwards / downwards

(e) y = ( x + 5) 2 − 2

(f) y = −( x + 1) 2 + 1

vertex:

vertex:

circle one: opens upwards / downwards

circle one: opens upwards / downwards

Once you come up with your answers, graph these parabolas on your graphing calculators and see if your answers are correct. If they aren’t, correct them in a different color and see if you can figure out where you went awry. (11) For each equation, answer what the vertex of the parabola is, and whether the parabola opens upwards or downwards. (a) y = ( x + 7) 2

(b) y = x 2 + 9

vertex:

vertex:

circle one: opens upwards / downwards

circle one: opens upwards / downwards

(c) y = − x 2 + 1

(d) y = −( x +V) 2 +W

vertex:

vertex:

circle one: opens upwards / downwards

circle one: opens upwards / downwards

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