Question

question 16 of 64 step 1 of 2 no time limit consider the following polynomial function: g(x) = x² - 2x - 8 step 1 of 2: plot the x-intercepts, if any, of the polynomial function on the graph. answer 3 points keypad keyboard shortcuts select the number of x-intercepts before plotting. you may move a point by dragging. number of x-intercepts none one two three four (graph with grid, x-axis from -10 to 10, y-axis from -5 to 10)

Explanation:

Step1: Recall x-intercept definition

To find x-intercepts, set \( g(x) = 0 \), so solve \( x^2 - 2x - 8 = 0 \).

Step2: Solve the quadratic equation

Factor the quadratic: \( x^2 - 2x - 8=(x - 4)(x + 2)=0 \).
Set each factor to zero: \( x - 4 = 0\) gives \( x = 4 \); \( x + 2 = 0\) gives \( x = -2 \).
So there are two x - intercepts.

Answer:

two (corresponding to the option "two")