Find the Vertex of the Graph of the Quadratic Function $f ( x ) = 2 x ^ { 2 } + 8 x$

question 184

Multiple Choice

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function.
- $f ( x ) = 2 x ^ { 2 } + 8 x$

• A) Vertex: \(( 0,8 )\); x-intercepts: none; y-intercept: \(( 0,8 )\)
• B) Vertex: \(( - 2 , - 8 )\); \(x\)-intercepts: \(( 0,0 )\) and \(( 4,0 )\); \(\mathrm { y }\)-intercept: \(( 0,0 )\)
• C) Vertex: \(( 0 , - 8 )\); \(x\)-intercepts: \(( - 2,0 )\) and \(( 2,0 )\); \(y\)-intercept: \(( 0 , - 8 )\)
• D) Vertex: \(( 2 , - 8 )\); \(x\)-intercepts: \(( 0,0 )\) and \(( 4,0 )\); \(y\)-intercept: \(( 0,0 )\)

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Definitions:

Elastic

Refers to the responsiveness of the quantity demanded or supplied of a good or service to a change in its price.

Demand Curve

A graphical representation showing the relationship between the price of a good and the quantity of that good consumers are willing to buy at various prices.

Monopolistic Competitors

Firms in a market structure where there are many producers selling products that are similar but not identical, allowing for a degree of market power and some control over prices.

Perfect Price Discrimination

A pricing strategy where a seller charges the maximum possible price for each unit consumed that the buyer is willing to pay, capturing all available consumer surplus.