Chapter 1.1, Problem 84AYU

In Problems 79-90, graph each equation by plotting points. Verify your results using a graphing utility.

$y=-x^2+1$

To determine

To sketch: The graph of the equation $y = -x^2 + 1$ by plotting points and then verify the results using a graphing utility.

Answer to Problem 84AYU

Explanation of Solution

Given:

The equation $y = -x^2 + 1$.

Interpretation:

$x = -2$	$y = -{(-2)}^2 +\mathrm{ 1} = -4 + 1 = -3$
$x = -1$	$y = -{(-1)}^2 +\mathrm{ 1} = -1 +\mathrm{ 1} = 0$
$x = 0$	$y = -{(0)}^2 +\mathrm{ 1} = 0 +\mathrm{ 1} = 1$
$x = 1$	$y = -{(1)}^2 +\mathrm{ 1} = -1 + 1 = 0$
$x = 2$	$y = -{(2)}^2 +\mathrm{ 1} = -4 +\mathrm{ 1} = -3$

The points on the graph $\left(-2,-3\right),\left(-1,0\right),\left(0,1\right),\left(1,0\right),\left(2,-3\right)$.