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

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

coffentw · Accepted Answer

Step 1 The parent function of P(x)=−x3+64 is y=x3, which passes through the points (−2,−8),(−1,−1),(0,0),(1,1)and(2,8). P(x)=−x3+64 is the graph of y=x3 reflected across the x-axis and then translated up 64 units. Reflecting the points on y=x3 across the x-axis gives (-2,8),(-1,1),(0,0),(1,-1) and (2,-8). Translating these points up 64 units then gives the points (-2,72), (-1,65),(0,64),(1,63), and (2,56). The x-intercept of P(x) is when P(x)=0: P(x)=−x3+64 Given function. 0=−x3+64 Substitute P(x)=0 x3=64 Add x3 on both sides. x=3{64} Cube root both sides. x=4 Simplify The x-intercept of P(x) is then the point (4,0). The y-intercept is when x=0 which we already know is at the point (0,64). Plot the points, including the x-intercept, and then connect them with a smooth curve. Label the coordinates of the intercepts in your graph:

Graph the polynomial by transforming an appropriate graph of the

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