Category 30 Example 1 - mental math
c/a = 3/4
Category 30 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 31 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 31 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 31 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 31 Example 3 Question 2 - may be mental math
-16t can be factored out simplifying the equation to t - 2 = 0 Hence, t = 2.
Category 32 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 32 Example 3 Question 2 - no calculation required
Max growth = y-coordinate of vertex that can be read from the graph.
Category 33 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 34 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 36 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.