Quadratics Review1) Vertex form. Complete the table for each quadratic relation.

Equation y = x2 + 7 y = 2(x – 1)2 + 3 y = ½ (x + 4) 2 - 2 y = -3(x – 5) 2

Vertex

Direction of opening

Min or max

Optimal Value

Equation of the Axis of SymmetryStep Pattern

2) Write the equation in vertex form, y = a(x-h)2 + k, for each parabola given the following:a) Vertex (1, 3), vertically stretched by a factor of 2, opens up.

___________________

b) Horizontal shift right 5 has a max of 8 ___________________

c) Vertex at (-2, 3), opens up, step pattern 0.5, 1.5, 2.5___________________

d) Reflected in the x axis, vertically stretched by a factor of 2, has an axis of symmetry of x = -3 and a min value of -3

___________________

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3) Graph the following quadratic relations (continue to the edge of the grid).a) y = -(x – 2)2 + 8 b) y = 2(x + 4)2 - 6

Vertex: _________ Vertex: __________

Direction of opening: _______ Direction of opening: _____

3 Steps of the step pattern: ___,___,___ 3 steps of the step pattern: ___,___,___

c) y= - ½(x - 5)2 - 3

Vertex: __________

Direction of opening: __________

3 Steps of the step pattern: ____,____,____

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4) For each graph below, write the equation in vertex form y = a(x-h)2 + k.

“a” value = ___ “a” value = ___direction: Up/Down direction: Up/DownVertex _______ Vertex _______y = _______________________ y = _________________________

5) Explain the transformations that would need to be done to the base parabola y=x2 to achieve each of the following parabolas.

Choose all appropriate words from the word bank

a) y=2 ( x−3 )2−5

_______________________________________________________

_______________________________________________________

_______________________________________________________

b) y=−13

(x+4)2

+6

______________________________________________________

_______________________________________________________

_______________________________________________________

_______________________________________________________

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Vertically, Vertical, Horizontal, Shift, Stretched, Compressed, by a factor of, reflected in the x axis, left, right, up, down, units

6) Gretchen is shoots a model airplane into the air, and it makes an arch formation. Its height, h, meters above the ground, after t seconds is h = -0.5( t – 5)2 + 4

a) How can you tell, from the equation, that the optimal height is a maximum?

b) What is the maximum height of the plane? _________

c) At what time does the plane reach this maximum height? _________

d) If the initial height of the place is 2m above the ground, ‘sketch’ the scenario on the grid here. Make sure to label the axes, include units and label important values.

7) The profit that a shoe manufacturer makes is related to the number of pairs of shoes ordered, as shown in the graph here.

a) What is the maximum profit

possible?

______________

b) How many shoes need to be was in order to make this profit? ______________

c) If the director would like to make above $2000 profit, how many shoes need to be sold?

At least ______________ but not more than _____________

d) By extending the graph, estimate how many pairs of shoes will cause the store to break even?

______&_______

e) What is the initial value of this relation? ___________ Is this a Profit or Loss?

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1 8. A wedding decorator wants to create a large arch for an outdoor wedding they are decorating. They want to build the arch in the shape of a parabola. The arch will be 3m tall at the centre. It will be vertically compressed by a factor of 0.5 and the two sides where the arch meet the ground will be 6m apart.

a.) How far over from where the arch hits the ground will it be at its peak? (explain/ show work).

b.) Give the equation that could be used to design the arch in vertex form.

9. Write the equation of the quadratic given the following information.

Vertex Step Pattern Direction of Opening Equation

(-1 , -8) 3, 9, 15 up

(0, -5) -1, -3, -5 down

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