Final answer:
To find the y-intercept of the function f(x) = -x³ - 3x² + 54x, substitute x = 0 into the function and solve for y. The y-intercept is 0. To find the x-intercepts of the given function, set the function equal to 0 and solve for x using factoring or the quadratic formula.
Step-by-step explanation:
The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations. An intercept is a point where the line or curve passes through the axis of the graph.
When a point crosses x axis then that point is called x intercept or horizontal intercept. And when that point crosses the y axis that point is called y intercept or vertical intercept.The y-intercept is the point where a graph intersects the y-axis, which occurs when x = 0.
To find the y-intercept of the function f(x) = -x³ - 3x² + 54x, substitute x = 0 into the function and solve for y: f(0) = -(0³) - 3(0²) + 54(0) = 0. Therefore, the y-intercept is 0. The x-intercepts are the points where a graph intersects the x-axis. To find the x-intercepts of the given function, set the function equal to 0 and solve for x: -x³ - 3x² + 54x = 0. Using factoring or the quadratic formula, you can find the x-intercepts of the function.