Understanding the Function Table

Oct 13, 2025 by talynt.org 96 views

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Understanding the Function Table

The given function table represents a relationship between two variables, x and y, where x is expressed as a function of y. The function is given by the equation x = 5y^2 + 3. The table contains three rows, each representing a specific value of y and the corresponding value of x.

y	x
0	3
2	23
4	?

Analyzing the Function Equation

To find the missing value in the table, we need to analyze the function equation x = 5y^2 + 3. This equation represents a quadratic function, where the coefficient of y^2 is 5 and the constant term is 3.

Substituting y = 4 into the Function Equation

To find the missing value in the table, we need to substitute y = 4 into the function equation x = 5y^2 + 3.

x = 5(4)^2 + 3 x = 5(16) + 3 x = 80 + 3 x = 83

Conclusion

Based on the analysis of the function equation and the substitution of y = 4, we can conclude that the missing value in the table is x = 83.

Comparison with Options

The calculated value of x = 83 is not among the given options. However, we can compare our result with the options provided.

Option	Value
A	23
B	43
C	403

Discussion

The given options do not match the calculated value of x = 83. This suggests that the options provided may not be correct or may be based on a different function equation.

Final Answer

Based on the analysis of the function equation and the substitution of y = 4, the final answer is x = 83.

Additional Information

The function equation x = 5y^2 + 3 represents a quadratic function with a positive leading coefficient. This means that the graph of the function is a parabola that opens upwards. The vertex of the parabola is the minimum point of the function, and the axis of symmetry is the vertical line that passes through the vertex.

Graph of the Function

The graph of the function x = 5y^2 + 3 is a parabola that opens upwards. The vertex of the parabola is at the point (0, 3), and the axis of symmetry is the vertical line x = 0.

Properties of the Function

The function x = 5y^2 + 3 has the following properties:

The function is a quadratic function with a positive leading coefficient.
The graph of the function is a parabola that opens upwards.
The vertex of the parabola is at the point (0, 3).
The axis of symmetry is the vertical line x = 0.

Conclusion

In conclusion, the missing value in the function table is x = 83. The function equation x = 5y^2 + 3 represents a quadratic function with a positive leading coefficient, and the graph of the function is a parabola that opens upwards.

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Q: What is the function equation given in the problem?

A: The function equation given in the problem is x = 5y^2 + 3.

Q: What is the relationship between x and y in the function equation?

A: The relationship between x and y in the function equation is that x is expressed as a function of y, where x = 5y^2 + 3.

Q: How do we find the missing value in the function table?

A: To find the missing value in the function table, we need to substitute the given value of y into the function equation and solve for x.

Q: What is the value of y that we need to substitute into the function equation?

A: The value of y that we need to substitute into the function equation is 4.

Q: What is the calculated value of x when y = 4?

A: The calculated value of x when y = 4 is x = 83.

Q: Why is the calculated value of x not among the given options?

A: The calculated value of x is not among the given options because the options provided may not be correct or may be based on a different function equation.

Q: What are the properties of the function x = 5y^2 + 3?

A: The properties of the function x = 5y^2 + 3 are:

The function is a quadratic function with a positive leading coefficient.
The graph of the function is a parabola that opens upwards.
The vertex of the parabola is at the point (0, 3).
The axis of symmetry is the vertical line x = 0.

Q: How do we graph the function x = 5y^2 + 3?

A: To graph the function x = 5y^2 + 3, we can use the properties of the function, such as the vertex and axis of symmetry, to draw the parabola.

Q: What is the significance of the axis of symmetry in the function x = 5y^2 + 3?

A: The axis of symmetry in the function x = 5y^2 + 3 is the vertical line x = 0, which passes through the vertex of the parabola. This means that the function is symmetric about the line x = 0.

Q: How do we determine the minimum point of the function x = 5y^2 + 3?

A: The minimum point of the function x = 5y^2 + 3 is the vertex of the parabola, which is at the point (0, 3).

Q: What is the relationship between the minimum point and the axis of symmetry of the function x = 5y^2 + 3?

A: The minimum point and the axis of symmetry of the function x = 5y^2 + 3 are related in that the axis of symmetry passes through the minimum point.

Q: How do we use the function x = 5y^2 + 3 to model real-world situations?

A: The function x = 5y^2 + 3 can be used to model real-world situations such as the motion of an object under the influence of gravity, where the height of the object is given by the function x = 5y^2 + 3.

Q: What are some common applications of the function x = 5y^2 + 3?

A: Some common applications of the function x = 5y^2 + 3 include:

Modeling the motion of an object under the influence of gravity
Describing the shape of a parabolic mirror or lens
Calculating the area and perimeter of a parabolic shape

Q: How do we use the function x = 5y^2 + 3 to solve problems in physics and engineering?

A: The function x = 5y^2 + 3 can be used to solve problems in physics and engineering by modeling the motion of objects, calculating the area and perimeter of parabolic shapes, and describing the shape of parabolic mirrors or lenses.