The Vertex of a Parabola Occurs Where the Derivative of Its

question 262

Multiple Choice

The vertex of a parabola occurs where the derivative of its equation is 0, so an equation associated with the equation of a
parabola can be solved to find the x-coordinate of the vertex. Find the vertex of the parabola, given the equation of the
parabola and its associated equation.
-Equation of parabola: $f ( x ) = 8 x ^ { 2 } + 32 x - 12$ ; associated equation: $0 = 16 x + 32$

• A) \(( - 2 , - 44 )\)
• B) \(( 2,84 )\)
• C) \(( - 2,84 )\)
• D) \(( 2 , - 44 )\)

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Definitions:

Equality

Equality refers to the state of being equal, especially in status, rights, and opportunities.

Total Surplus

Total surplus refers to the sum of consumer surplus and producer surplus in a market, representing the overall benefit that market participants gain from engaging in trade.

High-cost Producer

A producer or company which has higher costs of production compared to competitors, often due to inefficient processes or higher input costs.

Low-cost Producer

A manufacturer or service provider with a competitive advantage allowing them to offer goods or services at a lower price than competitors, often due to operational efficiencies.