This question is testing one's ability to compare the properties of functions when they are illustrated in different forms. This question specifically is asking for the examination and interpretation of two quadratic functions for which one is illustrated in a table format and the other is illustrated graphically.

For the purpose of Common Core Standards, "Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.9). 

Step 1: Identify the minimum of the table.

Using the table find the time value where the lowest distance exists. 

Recall that the time represents the  values while the distance represents the  values. Therefore the ordered pair for the minimum can be written as .

Step 2: Identify the minimum of the graph

Recall that the minimum of a parabola opening up, occurs at the valley where the vertex lies.

For this particular graph the vertex is at .

Step 3: Compare the minimums from step 1 and step 2.

Compare the  value coordinate from both minimums.

Therefore, the graph has the lowest minimum.

This question is testing one's ability to compare the properties of functions when they are illustrated in different forms. This question specifically is asking for the examination and interpretation of two quadratic functions for which one is illustrated in a table format and the other is illustrated graphically.

For the purpose of Common Core Standards, "Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.9). 

Step 1: Identify the maximum of Table 1.

Using the table find the time value where the largest distance exists. 

Recall that the time represents the  values while the distance represents the  values. Therefore the ordered pair for the maximum can be written as .

Step 2: Identify the maximum of the graph

Recall that the maximum of a cubic function is known as a local maximum. This occurs at the vertex of the peak on the graph which in this particular case, is at the point .

Step 3: Compare the maximums from step 1 and step 2.

Compare the  value coordinate from both maximums.

Therefore, the table has the largest maximum.

This question is testing one's ability to compare the properties of functions when they are illustrated in different forms. This question specifically is asking for the examination and interpretation of two quadratic functions for which one is illustrated in a table format and the other is illustrated graphically.

For the purpose of Common Core Standards, "Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.9). 

Step 1: Identify the maximum of Table 1.

Using the table find the time value where the largest distance exists. 

Recall that the time represents the  values while the distance represents the  values. Therefore the ordered pair for the maximum can be written as .

Step 2: Identify the maximum of the graph

Recall that the maximum of a parabola occurs at the vertex of the peak on the graph which in this particular case, is at the point 

Step 3: Compare the maximums from step 1 and step 2.

Compare the  value coordinate from both maximums.

Therefore, the table has the largest maximum.

This question is testing one's ability to compare the properties of functions when they are illustrated in different forms. This question specifically is asking for the examination and interpretation of two quadratic functions for which one is illustrated in a table format and the other is illustrated graphically.

For the purpose of Common Core Standards, "Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.9). 

Step 1: Identify the maximum of Table 1.

Using the table find the time value where the largest distance exists. 

Recall that the time represents the  values while the distance represents the  values. Therefore the ordered pair for the maximum can be written as .

Step 2: Identify the maximum of the graph

Recall that the maximum of a parabola occurs at the vertex of the peak on the graph which in this particular case, is at the point 

Step 3: Compare the maximums from step 1 and step 2.

Compare the  value coordinate from both maximums.

Therefore, the table has the largest maximum.

This question is testing one's ability to compare the properties of functions when they are illustrated in different forms. This question specifically is asking for the examination and interpretation of two quadratic functions for which one is illustrated in a table format and the other is illustrated graphically.

For the purpose of Common Core Standards, "Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.9). 

Step 1: Identify the minimum of the table.

Using the table find the time value where the lowest distance exists. 

Recall that the time represents the  values while the distance represents the  values. Therefore the ordered pair for the minimum can be written as .

Step 2: Identify the minimum of the graph

Recall that the minimum of a parabola opening up occurs at the valley where the vertex lies.

For this particular graph the vertex is at .

Step 3: Compare the minimums from step 1 and step 2.

Compare the  value coordinate from both minimums.

Therefore, the graph has the lowest minimum.

This question is testing one's ability to compare the properties of functions when they are illustrated in different forms. This question specifically is asking for the examination and interpretation of two quadratic functions for which one is illustrated in a table format and the other is illustrated graphically.

For the purpose of Common Core Standards, "Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.9). 

Step 1: Identify the maximum of Table 1.

Using the table find the time value where the largest distance exists. 

Recall that the time represents the  values while the distance represents the  values. Therefore the ordered pair for the maximum can be written as .

Step 2: Identify the maximum of the graph

Recall that the maximum of a cubic function is known as a local maximum. This occurs at the vertex of the peak on the graph which in this particular case, is at the point .

Step 3: Compare the maximums from step 1 and step 2.

Compare the  value coordinate from both maximums.

Therefore, the table has the largest maximum.

This question is testing one's ability to compare the properties of functions when they are illustrated in different forms. This question specifically is asking for the examination and interpretation of two quadratic functions for which one is illustrated in a table format and the other is illustrated graphically.

For the purpose of Common Core Standards, "Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.9). 

Step 1: Identify the minimum of the table.

Using the table find the time value where the lowest distance exists. 

Recall that the time represents the  values while the distance represents the  values. Therefore the ordered pair for the minimum can be written as .

Step 2: Identify the minimum of the graph

Recall that the minimum of a cubic function is known as a local minimum. This occurs at the valley where the vertex lies.

For this particular graph the vertex is at .

Step 3: Compare the minimums from step 1 and step 2.

Compare the  value coordinate from both minimums.

Therefore, the graph has the lowest minimum.

This question is testing one's ability to compare the properties of functions when they are illustrated in different forms. This question specifically is asking for the examination and interpretation of two quadratic functions for which one is illustrated in a table format and the other is illustrated graphically.

For the purpose of Common Core Standards, "Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.9). 

Step 1: Identify the maximum of Table 1.

Using the table find the time value where the largest distance exists. 

Recall that the time represents the  values while the distance represents the  values. Therefore the ordered pair for the maximum can be written as .

Step 2: Identify the maximum of the graph

Recall that the maximum of a cubic function is known as a local maximum. This occurs at the vertex of the peak on the graph which in this particular case, is at the point .

Step 3: Compare the maximums from step 1 and step 2.

Compare the  value coordinate from both maximums.

Therefore, the table has the largest maximum.

This question is testing one's ability to recognize functions in everyday situations and build the mathematical model that shows the relationship between two quantities. A question such as this requires examination into the behavior between the quantities, whether it be explicit expression, a recursive process, or a multi-step calculation. It also requires the use of algebraic operations to solve the question at hand and then build a function that models the relationship.

For the purpose of Common Core Standards, writing a function which describes a relationship falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

How many weeks will Sally need to work to earn enough money to buy the new computer?

Step 2: Identify what is given/known from the question.

The computer costs 

Sally earns 

Sally works 

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

From this model, substitute in the known values and solve for the weeks worked to answer the question.

Using algebraic operations divide by 64 on both sides to calculate the number of weeks Sally will need to work.

This question is testing one's ability to recognize functions in everyday situations and build the mathematical model that shows the relationship between two quantities. A question such as this requires examination into the behavior between the quantities, whether it be explicit expression, a recursive process, or a multi-step calculation. It also requires the use of algebraic operations to solve the question at hand and then build a function that models the relationship.

For the purpose of Common Core Standards, writing a function which describes a relationship falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.MATH.CONTENT.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

How many weeks will Jane need to work to earn enough money to buy the new backpack?

Step 2: Identify what is given/known from the question.

The backpack costs 

Jane earns 

Jane works 

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

From this model, substitute in the known values and solve for the weeks worked to answer the question.

Using algebraic operations divide by 12 on both sides to calculate the number of weeks Jane will need to work.