Solve each equation by graphing. Where necessary, round to the nearest hundredth
-x^3+2x^2+1=0
same as
x^3 - 2x^2 - 1 = 0
graph y = x^3 - 2x - 1 at
http://rechneronline.de/function-graphs/
just enter the function expression
x^3 - 2x - 1
To solve the equation -x^3 + 2x^2 + 1 = 0 by graphing, you would first plot the corresponding points on a graph.
1. Start by choosing a range of x-values to plot. Let's say we choose a range of -4 to 4.
2. Substitute these x-values into the equation to find the corresponding y-values. For example, when x = -4, plug it into the equation: -(-4)^3 + 2(-4)^2 + 1. Calculate this for multiple values of x.
3. Plot the points (x, y) on the graph.
4. Connect the points with a smooth curve. This curve represents the graph of the equation -x^3 + 2x^2 + 1 = 0.
5. Determine the x-coordinates of the points where the curve intersects the x-axis. These are the solutions to the equation.
6. If necessary, round the solutions to the nearest hundredth.
However, graphing by hand might be time-consuming, so it would be more efficient to use technology or a graphing calculator to plot the points and find the solutions.