Find the Vertex of the Graph of the Quadratic Function $f ( x ) = 10 + 7 x + x ^ { 2 }$

question 16

Multiple Choice

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function.
- $f ( x ) = 10 + 7 x + x ^ { 2 }$

• A) Vertex: \(\left( \frac { 7 } { 2 } , - \frac { 9 } { 4 } \right)\); \(x\)-intercepts: \(( - 2,0 )\) and \(( - 5,0 )\); y-intercept: \(( 0,10 )\)
• B) Vertex: \(\left( - \frac { 7 } { 2 } , - \frac { 9 } { 4 } \right)\); \(x\)-intercepts: \(( 2,0 )\) and \(( 5,0 )\); y-intercept: \(( 0,10 )\)
• C) Vertex: \(\left( \frac { 7 } { 2 } , - \frac { 9 } { 4 } \right)\); \(x\)-intercepts: \(( 2,0 )\) and \(( 5,0 )\); \(y\)-intercept: \(( 0,10 )\)
• D) Vertex: \(\left( - \frac { 7 } { 2 } , - \frac { 9 } { 4 } \right)\); \(x\)-intercepts: \(( - 2,0 )\) and \(( - 5,0 )\); \(y\)-intercept: \(( 0,10 )\)

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Definitions:

Activation Energy

The smallest quantity of energy necessary to start a chemical reaction.

Equilibrium

A state in a chemical reaction where the rates of the forward and reverse reactions are equal, leading to no overall change in the concentration of reactants and products.

Catalyst

A substance that increases the rate of a chemical reaction without being consumed or permanently altered in the process.

Equilibrium Constant

A numerical value that expresses the ratio of concentrations of products to reactants at equilibrium for a reversible chemical reaction at a constant temperature.