Question

(b) Find the x- and y-intercepts of the graph of the function.The x-intercept(s) is/are (c) Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept.The zero(s) of f is/are

Answer 1

$f(x)=x^2(x-10)(x+10)$

b) The function has three x-intercepts (when f(x) = 0): in x = -10, x = 0 and x = 10

It also has one y-intercept, in (x,y) = (0,0)

c) The least zero is a zero of multiplicity 1, so the graph of f crosses the x-axis at x = -10. The middle zero is a zero of multiplicity 2, so the graph of f touches the x-axis at x = 0. The gratest zero is a zero of multiplicity 1, so the graph of f crosses the x-axis at x = 10.