Athor8133idn
Answered

IDNLearn.com is your reliable source for expert answers and community insights. Discover the information you need quickly and easily with our reliable and thorough Q&A platform.

The table of values represents a quadratic function [tex]f(x)[/tex].

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$f(x)$[/tex] \\
\hline
-8 & 13 \\
\hline
-7 & 6 \\
\hline
-6 & 1 \\
\hline
-5 & -2 \\
\hline
-4 & -3 \\
\hline
-3 & -2 \\
\hline
-2 & 1 \\
\hline
-1 & 6 \\
\hline
0 & 13 \\
\hline
\end{tabular}

What is the equation of [tex]f(x)[/tex]?

A. [tex]f(x)=(x+5)^2-2[/tex]

B. [tex]f(x)=(x+4)^2-3[/tex]

C. [tex]f(x)=(x-4)^2-3[/tex]

Sagot :

GinnyAnsweridn
To determine the equation for the given quadratic function \( f(x) \) that matches the table of values, we need to compare each of the given possible equations with the values in the table. Here is a detailed step-by-step solution:

1. Identifying the Points from the Table:

The table presents the following points \((x, f(x))\):
[tex]\[ (-8, 13), (-7, 6), (-6, 1), (-5, -2), (-4, -3), (-3, -2), (-2, 1), (-1, 6), (0, 13) \][/tex]

2. Possible Equations:

We have three potential equations for \( f(x) \):
- \( f(x) = (x + 5)^2 - 2 \)
- \( f(x) = (x + 4)^2 - 3 \)
- \( f(x) = (x - 4)^2 - 3 \)

3. Testing the First Equation:

Let's test \( f(x) = (x + 5)^2 - 2 \):
- For \( x = -8 \): \( f(-8) = ((-8) + 5)^2 - 2 = (-3)^2 - 2 = 9 - 2 = 7 \) (not 13)

Since it does not match the first point, this equation is incorrect.

4. Testing the Second Equation:

Let's test \( f(x) = (x + 4)^2 - 3 \):
- For \( x = -8 \): \( f(-8) = ((-8) + 4)^2 - 3 = (-4)^2 - 3 = 16 - 3 = 13 \) (matches the table)
- For \( x = -7 \): \( f(-7) = ((-7) + 4)^2 - 3 = (-3)^2 - 3 = 9 - 3 = 6 \) (matches the table)
- For \( x = -6 \): \( f(-6) = ((-6) + 4)^2 - 3 = (-2)^2 - 3 = 4 - 3 = 1 \) (matches the table)
- For \( x = -5 \): \( f(-5) = ((-5) + 4)^2 - 3 = (-1)^2 - 3 = 1 - 3 = -2 \) (matches the table)
- For \( x = -4 \): \( f(-4) = ((-4) + 4)^2 - 3 = (0)^2 - 3 = 0 - 3 = -3 \) (matches the table)
- For \( x = -3 \): \( f(-3) = ((-3) + 4)^2 - 3 = (1)^2 - 3 = 1 - 3 = -2 \) (matches the table)
- For \( x = -2 \): \( f(-2) = ((-2) + 4)^2 - 3 = (2)^2 - 3 = 4 - 3 = 1 \) (matches the table)
- For \( x = -1 \): \( f(-1) = ((-1) + 4)^2 - 3 = (3)^2 - 3 = 9 - 3 = 6 \) (matches the table)
- For \( x = 0 \): \( f(0) = ((0) + 4)^2 - 3 = (4)^2 - 3 = 16 - 3 = 13 \) (matches the table)

Since all points match, this equation is correct.

5. Testing the Third Equation:

Let's test \( f(x) = (x - 4)^2 - 3 \):
- For \( x = -8 \): \( f(-8) = ((-8) - 4)^2 - 3 = (-12)^2 - 3 = 144 - 3 = 141 \) (not 13)

Since it does not match the first point, this equation is incorrect.

Given the checks above, the equation of \( f(x) \) that correctly matches all the values in the table is:
[tex]\[ f(x) = (x + 4)^2 - 3 \][/tex]
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Discover the answers you need at IDNLearn.com. Thank you for visiting, and we hope to see you again for more solutions.