Use the graph to solve y=2Xpower3 minus 3X power 2 minus 12X +5=10

To solve the equation $2x^3 - 3x^2 - 12x + 5 = 10$ using the graph, you need to find the $x$-values where the curve $y = 2x^3 - 3x^2 - 12x + 5$ intersects the horizontal line $y=10$.

We look for $x$-values where $y=10$. Using the table of values:

• The first intersection occurs between $x=-2$ (where $y=1$) and $x=-1$ (where $y=12$). Since $1 < 10 < 12$, there is a solution in this interval. Estimating from a graph, this value is approximately $x \approx -1.2$.

• The second intersection occurs between $x=-1$ (where $y=12$) and $x=0$ (where $y=5$). Since $5 < 10 < 12$, there is a solution in this interval. Estimating from a graph, this value is approximately $x \approx -0.7$.

• The third intersection occurs between $x=3$ (where $y=-4$) and $x=4$ (where $y=37$). Since $-4 < 10 < 37$, there is a solution in this interval. Estimating from a graph, this value is approximately $x \approx 3.3$.

The solutions to $2x^3 - 3x^2 - 12x + 5 = 10$ from the graph are approximately:

The solutions are $x \approx -1.2, -0.7, 3.3$.