Question - Finding Zeros and Y-intercept of a Factored Function
Solution:
The image displays a math problem related to finding the zeros of a function and the y-intercept of the function. The function is given in its factored form:f(x) = (x + 1)(x - 3)(x + 2)To find the zeros of the function, we need to set f(x) to 0 and solve for x. The zeros of a function are the x-values where the function crosses the x-axis (where f(x) = 0). Given that the function is already factored, the zeros are easily identified as the values that make each factor zero:x + 1 = 0 → x = -1x - 3 = 0 → x = 3x + 2 = 0 → x = -2Thus, the zeros of the function are x = -1, 3, and -2.To find the y-intercept of the function, we need to find the value of f(x) when x = 0. The y-intercept is the point where the graph of the function crosses the y-axis (the value of f(0)).f(0) = (0 + 1)(0 - 3)(0 + 2) = (1)(-3)(2) = -6Therefore, the y-intercept of the function is located at (0, -6).So, the correct answers to fill in the blanks would be:The zeros of the function f(x) = (x + 1)(x - 3)(x + 2) are -1, 3, and -2, and the y-intercept of the function is located at (0, -6).
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