You Are Given a Graph of a Function of the Form

question 120

Multiple Choice

You are given a graph of a function of the form $f ( x ) = a x ^ { 2 } + b x + c$ for different values of $a , b$ , and $c$ . For this function,
a. Determine whether the discriminant is positive, negative, or zero.
b. Determine if there are 0,1 , or 2 real solutions to $f ( x ) = 0$ .
c. Solve the equation $f ( x ) = 0$ .
-A ball is thrown downward from a window in a tall building. The distance traveled by the ball in t seconds is $$\mathrm { s } = 16 \mathrm { t } ^ { 2 } + 32 \mathrm { t }$$ where s is in feet. How long (to the nearest tenth) will it take the ball to fall 230 feet?

• A) 2.7 sec
• B) 2.9 sec
• C) 3.8 sec
• D) 8.4 sec

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Definitions:

Allocative Efficiency

A state in which resources are allocated in a way that maximizes the net benefit to society or achieves the desired distribution among competing uses.

Productive Efficiency

Productive efficiency occurs when an economy or entity produces goods and services at the lowest possible cost, utilizing all available resources without waste.

MB = MC

The principle that optimal decision-making is achieved when the marginal benefit equals the marginal cost.

Unintended Consequences

Outcomes of a policy or action that were not foreseen or intended, often contrary to the original objectives.