f(x) = x 2 + 4x + 4 For the given function f, what is the minimum value of f(x)?

Some values of x and the corresponding values of f(x) are given in the table shown.

If there is a linear relationship between x and f(x), which of the following equations gives this relationship?

In the right triangle PQR, the length of side $stack P Q with bar on top$ is 70, the measure of angle P is 90°, and the measure of angle R is 38°. Which of the following represents the length of side $stack Q R with bar on top$ ?

−x + y = −3.5
x + 3y = 9.5
If (x, y) satisfies the system of equations above, what is the value of y ?

The sum of −2x² + x + 31 and 3x² + 7x − 8 can be written in the form ax² + bx + c, where a, b, and c are constants. What is the value of a + b + c ?

x² + x − 12 = 0
If a is a solution of the equation above and a > 0, what is the value of a ?

In triangle RST above, point W (not shown) lies on $top enclose R T end enclose$ . What is the value of cos(∠RSW) − sin(∠WST) ?

kx+ y = 1
y = -x² + k
In the system of equations above, k is a constant. When the equations are graphed in the xy-plane, the graphs intersect at exactly two points. Which of the following CANNOT be the value of k ?

$x minus 1 half a equals 0$
If x = 1 in the equation above, what is the value of a ?

(x − 6)² + (y + 5)² = 16
In the xy-plane, the graph of the equation above is a circle. Point P is on the circle and has coordinates (10, −5). If $top enclose P Q end enclose$ is a diameter of the circle, what are the coordinates of point Q ?

f (x) = x³ - 9x
g(x) = x² - 2x - 3
Which of the following expressions is equivalent to $fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction comma text for end text x greater than 3$ ?

x

g(x)

-2

1

-1

2

0

3

1

4

2

5

3

6

4

7

The complete graph of the function f and a table of values for the function g are shown above. The maximum value of f is k. What is the value of g(k)?

Volume $equals fraction numerator 7 pi k cubed over denominator 48 end fraction$

The glass pictured above can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces.
Jenny has a pitcher that contains 1 gallon of water. How many times could Jenny completely fill the glass with 1 gallon of water? (1 gallon = 128 fluid ounces)

$K equals fraction numerator 200 v squared over denominator 2 end fraction$
In the equation above, the kinetic energy, K, of a 200-gram object is given in terms of its speed, v. If the equation is rewritten in the form v = $a square root of K$ , where a is a positive constant, what is the value of a ?

In the xy-plane, the point (p, r) lies on the line with equation y = x + b, where b is a constant. The point with coordinates (2p, 5r) lies on the line with equation y = 2x + b. If p ≠ 0, what is the value of $r over p$ ?

If we have coordinates of two points on a line, then we can use the slope formula to determine that line's slope. m = (y₂-y₁) / (x₂-x₁), or the ratio of the change in the y values and the x values, is the slope formula. 'x₁' and 'y₁' are the coordinates of the first point. The second points have the coordinates x₂ and y₂. If you have two points, you can always calculate the slope of a line. If you don't have access to two points, you can locate two points on the graph and use those to calculate the slope.
¶Observe the following helpful information:
- m = slope
¶-Rise = the difference between the y-values (y₂- y₁), where (x₁, y₁) = point 1 and (x₂, y₂) = point 2.
Run is equal to the difference between x-values (x₂ - x₁).

In the xy-plane, the point (p, r) lies on the line with equation y = x + b, where b is a constant. The point with coordinates (2p, 5r) lies on the line with equation y = 2x + b. If p ≠ 0, what is the value of $r over p$ ?