Question

f(x) = x² - 3x - 4
step 1 of 2: plot the x-intercepts, if any, of the polynomial function on the graph.
answer 3 points
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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 x-axis from -10 to 10, y-axis from -5 to 10, grid lines)

Explanation:

Step1: Find x-intercepts

To find the \( x \)-intercepts, set \( f(x) = 0 \), so solve \( x^2 - 3x - 4 = 0 \).

Step2: Factor the quadratic

Factor the equation: \( x^2 - 3x - 4=(x - 4)(x + 1)=0 \).

Step3: Solve for x

Set each factor equal to zero: \( x - 4 = 0 \) gives \( x = 4 \), and \( x + 1 = 0 \) gives \( x=-1 \). So there are two \( x \)-intercepts.

Answer:

two (corresponding to the option "two")