Use the following information to answer the next question:

A farmer has 20 windmill generators that produce an average of 300 watts of electricity each. The farmer wants to increase the number of generators he has. For each generator that is added, 10 watts are lost from each of the generators. To determine the number of generators that should be added to maximize total power production, the farmer uses a quadratic function and completes the square.

Total power	(P) = (number of generators)(watts per generator)
	x = number of additional generators
p = (20 + x) (300 - 10x)
p = -10x2 + 100x + 6000
p = -10(x - 5)2 + 6250

To maximize total power production, the number of generators that the farmer should add is    i    and the total power produced will be    ii    watts.

The statement above is completed by the numbers below:

The snowboard terrain park features several “quarter pipes.” A quarter pipe is created by molding snow into the shape of a partial parabola, as modeled in the graph below. This shape can be represented by the function:

If point (0,0) and point (3,1.8) represent the vertex and top of the snow bank respectively, then a quadratic function that represents the shape of the quarter pipe is:

A student used the following steps to complete the square of the quadratic function
Y = x² + 6x - 6.

Step 1	y = (x2 + 6x) - 6
Step 2	y = (x2 + 6x + 9) - 6 + 9
Step 3	y = (x + 3)2 + 3
Step 4	The vertex is (-3,3)

The student first made an error in:

Four graphs of y = ax² are shown below:


When the graphs are arranged so that the values of a are listed from smallest to largest, their order is      ,      ,      and     .

Use the following information to answer the next question:

To convert the quadratic function y = -2x² + 4x + 13 into the completed square form y = a(x – h)² + k, a student performed the following steps:

Step 1	y = -2(x2 – 2x) + 13
Step 2	y = -2(x2 – 2x + 1) + 13 + 2
Step 3	y = -2(x2 – 2x + 1) + 15
Step 4	y = -2(x + 1)2 +15

The student made an error in:

A farmer wants to plant sunflower seeds in rows that are 1m apart. To determine the rate of seeding for sunflowers, the farmer analyzes the relationship between the seed spacing in each row, in metres, and the expected sunflower plant density, in plants/m², as shown in the graph below.


If the farmer wants to get a sunflower plant density of 5 plants/m², then the seed spacing in each row, correct to the nearest tenth of a metre, needs to be       m.

Use the following information to answer the next question.

The graph of a quadratic function is shown below.


The roots of a quadratic equation may be found by examining the graph of its corresponding function.

The roots of the quadratic equation corresponding to the function of the graph above are:

To solve the quadratic equation 5x² - 10x - 21 = 0, a student used the quadratic formula and got the following partial answer:



In this equation, the values for x, to the nearest hundredth, are:

The inverse of the function y = 3x – 6 is:

In a rational expression, non-permissible values are values that make the

The graph of the quadratic function f(x) = x² and the graph of the transformed function y = g(x) are shown below:


The function y = g(x) can be expressed as:

If the graph of y = x² were shifted left 7 units and up 4 units, then the axis of symmetry of the transformed graph would be:

The y-intercept of the graph of the function y = 0.5(x – 9.0)², to the nearest tenth, is:

Use the following information to answer the next question.

The equation y = -(x - 3)² + 4 was graphed, as show below.


The x-intercepts of the graphed function are:

Points A(1, k) and B(-2, k) lie on the graph of the polynomial function p(x) = 3x³ + ax² + 1. A student is asked to find the value of a. The student evaluates P(1) to obtain

3 + a + 1 = k

4 + a = k

If the student correctly completes her work, then she will find the value of a to be:

A bicycle designer developing an aerodynamic bike frame used a parabolic shape, as shown below. To analyze aspects of the parabolic shape, the designer rotated the curve and graphed it on a coordinate plane.


The quadratic function representing the graph of the parabolic shape above is

y = -0.2(x – 12.0)² + 28.8, where x and y are distances, in centimeters.

On the graph above, the distance between the two x-intercepts, point O and point P, correct to the nearest tenth of a centimeter, is: