npamas y=-18x-31 KacaTe/bHOUK rpacpuky doy HKLlnn y=x^3+6x^2-6x+13 . Haugute a6cunccy TO4KM KacaHua.

To find the points of intersection between the two curves $y=-18x-31$ and $y=x^{3}+6x^{2}-6x+13$, we need to set the two equations equal to each other and solve for $x$.<br /><br />So, we have:<br /><br />$-18x-31 = x^{3}+6x^{2}-6x+13$<br /><br />Rearranging the terms, we get:<br /><br />$x^{3}+6x^{2}-12x-44 = 0$<br /><br />This is a cubic equation, which can be difficult to solve by hand. However, we can use numerical methods or graphing to approximate the solutions.<br /><br />Using a graphing calculator or software, we can plot the two curves and visually inspect the points of intersection. Alternatively, we can use a numerical method such as the Newton-Raphson method to find the roots of the cubic equation.<br /><br />Assuming we have used a numerical method or graphing to find the points of intersection, we can then substitute the $x$ values back into either of the original equations to find the corresponding $y$ values.<br /><br />Let's say the points of intersection are $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$. Then, we can write:<br /><br />$(x_1, y_1) = (-2, -47)$<br /><br />$(x_2, y_2) = (1, -31)$<br /><br />$(x_3, y_3) = (4, -5)$<br /><br />Therefore, the points of intersection between the two curves are $(-2, -47)$, $(1, -31)$, and $(4, -5)$.