Section 6 - Absolute Value (Edition 1)

---

Category 38 Example 2 - mental math

The midpoint of the two numbers can be determined using mental math = 65. Match this to the expression within the absolute value pipes.

The distance of the midpoint from each number will be same and can be determined using mental math = 15. Match it to the number that is right of the inequality operator.

---

Category 39 Example 1 - no calculation required

The shift of the vertex (right, left, up, down) from (0, 0) can be determine by looking at the graph. Match this shift to the vertex in the answer choices.

Category 39 Example 2 - mental math

Look at the values of f(x) from the table for the two values of x and subtract. Absolute value is always positive. Hence |-3| = 3.

Section 5 - Quadratic Equations and Parabola (Edition 1)

---

Category 29 Example 1 - mental math

c/a = 3/4

Category 29 Example 2 - mental math, depending on comfort level

Sum of roots from equation = -9/2 = -4.5

Since one root is given as -5, the other root must be 0.5 (same as 1/2) for sum to equal -4.5.

---

Category 30 Example 1 - no calculation required

The y-intercept from the graph = 4 and a is negative since the parabola opens downwards. Eliminate answer choices that don't match this.

Category 30 Example 2 - mental math

Step 1: -b/2a can be calculated using mental math. Eliminate answer choices C and D that do not match the value of x.

Step 2: When x=-1 is plugged in the equation, 12x will be -12. This is greater than 6 + 4. Hence, y must be negative. This eliminates answer choice B.

Category 30 Example 3 Question 1 - mental math

Step 1: -b/2a can be calculated using mental math.

Step 2: Since the value of x is small, this step can be done using mental math.

Category 30 Example 3 Question 2 - may be mental math

-16t can be factored out simplifying the equation to t - 2 = 0 Hence, t = 2.

---

Category 31 Example 3 Question 1 - no calculation required

Vertex can be directly read from the graph. Since the parabola opens downwards a is negative. Match this to answer choices. Only one answer choice has the matching vertex and negative a.

Category 31 Example 3 Question 2 - no calculation required

Max growth = y-coordinate of vertex that can be read from the graph.

---

Category 32 Example 1 - mental math

Calculation of midpoint formula can be done using mental math: (6-2)/2 =2.

Since the value of x is small, the calculation for y can also be done by mental math: (-4)(4) = -16.

---

Category 33 Example 1 - mental math and shortcut. (There is no need for "complete the square" method.)

Step 1- mental math:

Eliminate answer choices that don't have a value matching the given equation.

Determine the x-coordinate of the vertex from the given equation as -b/2a. Match it to the x-coordinate of the vertex in answer choices.

In some questions, this may eliminate all 3 incorrect answer choices. If not, the remaining incorrect answer choices (usually 1 of the 2 remaining) may be eliminated using a shortcut as shown in Step 2.

Step 2 - may be shortcut and mental math depending on comfort level, otherwise use Step 2 shown in the book: It may seem confusing at first but try it to see that it is not. If a = 1, the correct answer choice may be apparent by eyeballing.

Pick one of the remaining answer choice. Square the value of h and multiply it by the value of a if a > 1. Add this number to the value of k. If it matches the value of c in the given equation it is the correct answer choice. If not, the remaining answer choice is the correct answer.

Tip: shortcut = (h squared x a) + k

---

Category 35 Example 2 - no calculation required

When the question gives a graph and the answer choices are in vertex form, the transformation of the vertex can be directly read from the graph and matched with answer choices.

Section 4 - Polynomial Functions (Edition 1)

---

Category 22 Example 1 - no calculation required

The values can be directly read from the table. The f(x) value for a certain value of x can be read from the corresponding f(x) column. The x value for a certain value of f(x) can be read from the corresponding x column.

Category 22 Example 2 - no calculation required

It can be observed from the graph that for x = -1, the value of y = 2. Count the number of times the graph intersects the x-axis at y = -2.

---

Category 23 Example 2 - no calculation required.

The value of g(4) can be read from the table as -6. The value of f(-6) can be read from the table as 12.

---

Category 24 Example 1 - no calculation required

The points where the graph passes through the x-axis or touches the x-axis can be directly read from the graph.

Tip: Passes through = 1 factor. Touches and curves back = 2 identical factors.

Category 24 Example 2 - no calculation required

Each factor is a distinct zero. Count them.

Category 24 Example 3 - no calculation required

From the x column read the values where h(x) = 0

Tip: y = 0 at x-intercept.