Solve the equation
y = x ^ 3 - 5x ^ 2 + 2x + 8
Give the x-interecept and y-intercept and show it on a graph
clearly, x=0 is not an x-intercept. since y(0) = 8
x^3 - 5x^2 + 2x + 8 = (x+1)(x-2)(x-4)
so the x-intercepts are at x = -1,2,4
You are correct, my apologies for the mistake. The x-intercepts are indeed at x = -1, 2, and 4. Thank you for pointing that out.
Here is the corrected graph:
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y-axis
The x-intercepts are indicated by the points (-1, 0), (2, 0), and (4, 0).
The y-intercept is still 8, as previously calculated.
Again, I apologize for the error and thank you for bringing it to my attention.
To find the x-intercept, we need to set y equal to zero:
0 = x^3 - 5x^2 + 2x + 8
We can solve this equation by factoring, using the Rational Root Theorem, or by graphing. Since we have been asked to graph the equation, we will use the graphing method to find the x-intercept:
First, plot the graph of the equation by selecting some x-values and calculating the corresponding y-values:
x = -3, y = (-3)^3 - 5(-3)^2 + 2(-3) + 8 = -1
x = -2, y = (-2)^3 - 5(-2)^2 + 2(-2) + 8 = 10
x = -1, y = (-1)^3 - 5(-1)^2 + 2(-1) + 8 = 13
x = 0, y = 8
x = 1, y = 6
x = 2, y = (-2)
x = 3, y = 16
(Note: These points were calculated using the equation y = x^3 - 5x^2 + 2x + 8)
Now, we can plot these points on a graph:
(Assume x-axis is horizontal and y-axis is vertical)
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y-axis
The x-intercepts are the points where the graph intersects the x-axis. From the graph, we can see that the x-intercepts are approximately -3, 0, and 3.
For the y-intercept, we need to find the value of y when x is equal to zero. We substitute x = 0 into the equation:
y = (0)^3 - 5(0)^2 + 2(0) + 8 = 8
Therefore, the y-intercept is 8.
In summary:
- X-intercepts: approximately -3, 0, and 3
- Y-intercept: 8
Please note that the graph is just an approximation and not to scale.