Q 9. - Precalculus Enhanced with Graphing Utilities

Question

List the intercepts and test for symmetry: $x^2+y=9$.

Step-by-Step Solution

Answer

The equation is identical to the original equation it is symmetric to $y$ axis.

The graph if the line shown below.

Step 1. Given information.

Consider the given equation $x^2+y=9$.

Step 2. If x , y exist on graph then the graph is symmetric about x -axis , y -axis and origin.Showing the line is symmetric about y axis.

To show that the line is symmetric to $y$ axis put $-x$ in place of $x$.

$y=-{\left(-x\right)}^2+9$

$y=-x^2+9$

Since the equation is in original form so it is symmetric to $y$ axis.

 

Step 3. List the intercept.

$x$	$y$	$\left(x,y\right)$
$0$	$9$	$\left(0,9\right)$
$1$	$8$	$\left(1,8\right)$
$2$	$5$	$\left(2,5\right)$
$3$	$0$	$\left(3,0\right)$

Step 4. plot the graph.

The graph for the given equation$x^2+y=9$ is shown below.