Complete The Table For The Function F ( B ) = B 2 + 2 B − 9 F(b) = B^2 + 2b - 9 F ( B ) = B 2 + 2 B − 9 . \[ \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{ F(b) = B^2 + 2b - 9 } \\ \hline B$ & F ( B ) F(b) F ( B ) \ \hline -3 & □ \square □ \ \hline -2 & □ \square □ \ \hline -1 & □ \square □

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Completing the Table for the Quadratic Function f(b)=b2+2b−9f(b) = b^2 + 2b - 9

In this article, we will focus on completing the table for the given quadratic function f(b)=b2+2b−9f(b) = b^2 + 2b - 9. The table will contain the values of bb and the corresponding values of f(b)f(b).

Understanding the Quadratic Function

A quadratic function is a polynomial function of degree two, which means the highest power of the variable is two. The general form of a quadratic function is f(x)=ax2+bx+cf(x) = ax^2 + bx + c, where aa, bb, and cc are constants. In this case, the quadratic function is f(b)=b2+2b−9f(b) = b^2 + 2b - 9.

Completing the Table

To complete the table, we need to find the values of f(b)f(b) for the given values of bb. We will substitute the values of bb into the function and simplify to find the corresponding values of f(b)f(b).

Substituting b=−3b = -3

f(−3)=(−3)2+2(−3)−9f(-3) = (-3)^2 + 2(-3) - 9 f(−3)=9−6−9f(-3) = 9 - 6 - 9 f(−3)=−6f(-3) = -6

Substituting b=−2b = -2

f(−2)=(−2)2+2(−2)−9f(-2) = (-2)^2 + 2(-2) - 9 f(−2)=4−4−9f(-2) = 4 - 4 - 9 f(−2)=−9f(-2) = -9

Substituting b=−1b = -1

f(−1)=(−1)2+2(−1)−9f(-1) = (-1)^2 + 2(-1) - 9 f(−1)=1−2−9f(-1) = 1 - 2 - 9 f(−1)=−10f(-1) = -10

The Completed Table

bb f(b)f(b)
-3 -6
-2 -9
-1 -10

Discussion

The completed table shows the values of f(b)f(b) for the given values of bb. We can see that the function is decreasing as the value of bb increases. This is because the coefficient of the b2b^2 term is positive, which means the function is concave up.

Conclusion

In this article, we completed the table for the quadratic function f(b)=b2+2b−9f(b) = b^2 + 2b - 9. We substituted the values of bb into the function and simplified to find the corresponding values of f(b)f(b). The completed table shows the values of f(b)f(b) for the given values of bb.

Additional Examples

Substituting b=0b = 0

f(0)=(0)2+2(0)−9f(0) = (0)^2 + 2(0) - 9 f(0)=−9f(0) = -9

Substituting b=1b = 1

f(1)=(1)2+2(1)−9f(1) = (1)^2 + 2(1) - 9 f(1)=1+2−9f(1) = 1 + 2 - 9 f(1)=−6f(1) = -6

Substituting b=2b = 2

f(2)=(2)2+2(2)−9f(2) = (2)^2 + 2(2) - 9 f(2)=4+4−9f(2) = 4 + 4 - 9 f(2)=−1f(2) = -1

The Completed Table with Additional Examples

bb f(b)f(b)
-3 -6
-2 -9
-1 -10
0 -9
1 -6
2 -1

Final Discussion

The completed table with additional examples shows the values of f(b)f(b) for a wider range of values of bb. We can see that the function is still decreasing as the value of bb increases. This is because the coefficient of the b2b^2 term is positive, which means the function is concave up.

Conclusion

In our previous article, we completed the table for the quadratic function f(b)=b2+2b−9f(b) = b^2 + 2b - 9. In this article, we will answer some frequently asked questions about the quadratic function.

Q: What is the general form of a quadratic function?

A: The general form of a quadratic function is f(x)=ax2+bx+cf(x) = ax^2 + bx + c, where aa, bb, and cc are constants.

Q: What is the coefficient of the b2b^2 term in the quadratic function f(b)=b2+2b−9f(b) = b^2 + 2b - 9?

A: The coefficient of the b2b^2 term is 1.

Q: What is the coefficient of the bb term in the quadratic function f(b)=b2+2b−9f(b) = b^2 + 2b - 9?

A: The coefficient of the bb term is 2.

Q: What is the constant term in the quadratic function f(b)=b2+2b−9f(b) = b^2 + 2b - 9?

A: The constant term is -9.

Q: What is the value of f(b)f(b) when b=−3b = -3?

A: The value of f(b)f(b) when b=−3b = -3 is -6.

Q: What is the value of f(b)f(b) when b=−2b = -2?

A: The value of f(b)f(b) when b=−2b = -2 is -9.

Q: What is the value of f(b)f(b) when b=−1b = -1?

A: The value of f(b)f(b) when b=−1b = -1 is -10.

Q: Is the quadratic function f(b)=b2+2b−9f(b) = b^2 + 2b - 9 increasing or decreasing?

A: The quadratic function f(b)=b2+2b−9f(b) = b^2 + 2b - 9 is decreasing.

Q: Why is the quadratic function f(b)=b2+2b−9f(b) = b^2 + 2b - 9 decreasing?

A: The quadratic function f(b)=b2+2b−9f(b) = b^2 + 2b - 9 is decreasing because the coefficient of the b2b^2 term is positive, which means the function is concave up.

Q: What is the vertex of the quadratic function f(b)=b2+2b−9f(b) = b^2 + 2b - 9?

A: The vertex of the quadratic function f(b)=b2+2b−9f(b) = b^2 + 2b - 9 is at the point (−1,−10)(-1, -10).

Q: How can we find the vertex of a quadratic function?

A: We can find the vertex of a quadratic function by using the formula x=−b2ax = -\frac{b}{2a}.

Q: What is the x-intercept of the quadratic function f(b)=b2+2b−9f(b) = b^2 + 2b - 9?

A: The x-intercept of the quadratic function f(b)=b2+2b−9f(b) = b^2 + 2b - 9 is at the point (3,0)(3, 0).

Q: How can we find the x-intercept of a quadratic function?

A: We can find the x-intercept of a quadratic function by setting f(x)=0f(x) = 0 and solving for xx.

Conclusion

In this article, we answered some frequently asked questions about the quadratic function f(b)=b2+2b−9f(b) = b^2 + 2b - 9. We hope that this article has been helpful in understanding the quadratic function.

Additional Resources

Final Discussion

The quadratic function f(b)=b2+2b−9f(b) = b^2 + 2b - 9 is a simple quadratic function that can be used to model a wide range of real-world phenomena. We hope that this article has been helpful in understanding the quadratic function and its properties.

Conclusion

In this article, we completed the table for the quadratic function f(b)=b2+2b−9f(b) = b^2 + 2b - 9 and answered some frequently asked questions about the quadratic function. We hope that this article has been helpful in understanding the quadratic function.