Put brackets around the first two terms on the right. y = (-4x^2 - 16x) - 14
Pull out the common factor in the first two terms. y = -4(x^2 + 4x) - 14
Divide the middle term by 2. Add that inside the brackets. square y = -4(x^2 +4x +(4/2)^2 - 14
y = -4(x^2 + 4x + 4) - 14 + 16 This is the step where most people stumble. The point is why is 16 added? It is because what you have done inside the brackets is multiplied 4 by - 4 (on the left). That means you have changed the equation by -16. To counter that, you must add 16 after the - 14. The result is y= -4(x^2 + 4x+4) + 2
Express the terms inside the brackets as a square. y = - 4(x + 2)^2 + 2
B and D are both wrong. B has +4 outside the brackets. It is - 4
D is wrong because there is no 4 of any kind outside the brackets.
A is incorrectly represented inside the brackets as 16. That's not right
That only leaves C. <<<< Answer
Graphs
Notice that the red parabola and the green one are the same thing.
a. A consumer testing service is commissioned to rank the top 5 brands of dishwasher detergent. Nine brands are to be included in the study. In how many different ways can the consumer testing service arrive at the ranking?
b. A group of 12 people is traveling in three vehicles. If 4 people ride in each vehicle, in how many different ways can the people be assigned to the vehicles?
25 is equivalent to 820 because 2 x 20 = 5 x 8 = 40. 410 is equivalent to 820 because 4 x 20 = 10 x 8 = 80. 615 is equivalent to 820 because 6 x 20 = 15 x 8 = 120.