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Finding the Zeros and Intercepts of
To find the zeros and intercepts of the quadratic function :
Finding the zeros: Set the function equal to zero, . Factor the trinomial to obtain . Apply the zero product property by setting each factor to zero ( or ), which yields the solutions and .
Finding the x-intercepts: An x-intercept occurs when the function's value is zero (). Since and , the x-intercepts of the graph are the points and .
Finding the y-intercepts: A y-intercept occurs when . Substitute for to find , which simplifies to . Therefore, the y-intercept is the point .
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Finding the Zeros and Intercepts of
Finding the Zeros and Intercepts of
Finding the Zeros and Intercepts of
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A production team is analyzing an efficiency model defined by the function to determine when the system output reaches exactly zero. After setting the function equal to zero (), they factor the trinomial to find the solutions. One of the binomial factors is and the other factor is ____.