Select the correct answer. The table represents quadratic function g. Which statement is true about the function?
A. The maximum occurs at the function’s x-intercept.
B. The minimum occurs at the function’s x-intercept.
C. The maximum occurs at the function’s y-intercept.
D. The minimum occurs at the function’s y-intercept.
To determine the correct answer, we need to recall the properties of a quadratic function, which can be expressed in standard form as ( g(x) = ax^2 + bx + c ).
1. If ( a > 0 ), the function opens upwards and has a minimum point (the vertex) but no maximum.
2. If ( a < 0 ), the function opens downwards and has a maximum point (the vertex) but no minimum.
The x-intercepts are the points where ( g(x) = 0 ) and the y-intercept is found at ( g(0) ).
– A and B involve x-intercepts, but the vertex (maximum or minimum) does not occur at the x-intercept.
– C and D involve the y-intercept; again, the vertex does not occur at the y-intercept.
Since we don’t have specifics on whether the function opens upwards or downwards, we can’t definitively choose between C or D based solely on the general rules.
Thus, if the question allows for specific information about the function (like the leading coefficient), answer based on that; otherwise, for a general case, the maximum or minimum does not occur at the intercepts.
I encourage you to refer to the extended services page for detailed assistance or insights!