Q. 68 - Precalculus Enhanced with Graphing Utilities

Question

If $(a,-5)$ is a point on the graph of $y=x^2+6x$, what is $a$?

Step-by-Step Solution

Answer

The value of $a$ is $-5$ or $-1$.

Step 1: Given information

The given point is $\left(a,-5\right)$.

The given equation is $y=x^2+6x$.

Step[ 2: Determine the value of a .

Substitute $a$ for $x$, $-5$ for $y$ in $y=x^2+6x$.

$\begin{array}{rcl}-5& =& a^2+6a\\ a^2+6a+5& =& 0\\ a^2+5a+a+5& =& 0\\ a\left(a+5\right)+1\left(a+5\right)& =& 0\\ \left(a+1\right)\left(a+5\right)& =& 0\\ a& =& -5,-1\end{array}$

Step 3: Write the conclusion

The value of $a$ is $-5$ or $-1$.