Q. 67 - Precalculus Enhanced with Graphing Utilities

Question

If $(a, 4)$ is a point on the graph of $y=x^2+3x$, what is $a$?

Step-by-Step Solution

Answer

The value of $a$ is $-4$ or $1$.

Step 1: Given information

The given point is $\left(a,4\right)$.

The given equation is $y=x^2+3x$.

Step 2: Determine the value of a

Substitute $a$ for $x$, $4$ for $y$ in $y=x^2+3x$.

$\begin{array}{rcl}4& =& a^2+3a\\ a^2+3a-4& =& 0\\ a^2+4a-a-4& =& 0\\ a\left(a+4\right)-1\left(a+4\right)& =& 0\\ \left(a-1\right)\left(a+4\right)& =& 0\\ a& =& -4,1\end{array}$

Step 3: Write the conclusion

The value of $a$ is $-4$ or $1$.