Example 5
Completion requirements
| Example 5 |
Change \(f\left( x \right) = x^2 + 6x + 3\) to vertex form. Verify the answer using your graphic calculator.
\(\begin{array}{l}
f\left( x \right) = x^2 + 6x + 3 \\
f\left( x \right) = \left( {x^2 + 6x} \right) + 3 \\
f\left( x \right) = \left( {x^2 + 6x + 9 - 9} \right) + 3 \\
f\left( x \right) = \left( {x^2 + 6x + 9} \right) + 3 - 9 \\
f\left( x \right) = \left( {x + 3} \right)^2 - 6 \\
\end{array}\)
To verify your work using technology, enter into the calculator the function in standard form and the function in vertex form, and then graph them. Change the second graph to a darker shading. When graphing, the second graph should be drawn over top of the first graph. If two different graphs are formed, then an error was made. Observe the following screen captures.
The first screen capture shows that both forms have been entered into the calculator, and the second screen capture shows the second graph being drawn directly on top of the first graph. Completing the square was done correctly.
f\left( x \right) = x^2 + 6x + 3 \\
f\left( x \right) = \left( {x^2 + 6x} \right) + 3 \\
f\left( x \right) = \left( {x^2 + 6x + 9 - 9} \right) + 3 \\
f\left( x \right) = \left( {x^2 + 6x + 9} \right) + 3 - 9 \\
f\left( x \right) = \left( {x + 3} \right)^2 - 6 \\
\end{array}\)
To verify your work using technology, enter into the calculator the function in standard form and the function in vertex form, and then graph them. Change the second graph to a darker shading. When graphing, the second graph should be drawn over top of the first graph. If two different graphs are formed, then an error was made. Observe the following screen captures.
The first screen capture shows that both forms have been entered into the calculator, and the second screen capture shows the second graph being drawn directly on top of the first graph. Completing the square was done correctly.