Question

Graph the polynomial by transforming an appropriate graph of the form y=xⁿ. Show clearly all x - and y -intercepts. P(x)=-x³+64

Answer 1

To graph the polynomial P(x) = -x³ + 64, find the x and y-intercepts and use them to plot the curve.

Step-by-step explanation:

To graph the polynomial P(x) = -x³ + 64, we can transform the graph of y = xⁿ by adjusting the constants. First, let's find the x-intercepts by setting P(x) equal to zero and solving for x:

-x³ + 64 = 0

x³ = 64

x = 4

So, the x-intercept is (4, 0). Next, let's find the y-intercept by substituting x = 0 into the equation:

P(0) = -0³ + 64

P(0) = 64

So, the y-intercept is (0, 64). Now, let's plot these points on a graph and sketch the curve, taking into account the transformation.