Zander was given two functions: the one represented by the graph and the function f(x) = (x + 4)2. What can he conclude about the two functions?They have the same vertex.They have one x-intercept that is the same.They have the same y-intercept.They have the same range.
C They have the same y-intercept.
Zander can conclude that the two functions represented by the graph and f(x) = (x + 4)2 have the same vertex.
The vertex of the function f(x) = (x + 4)2 can be found by rewriting the function in vertex form, which is f(x) = a(x – h)2 + k, where (h, k) is the vertex of the parabola. Rewriting f(x) in this form gives f(x) = 1(x + 4)2 + 0, which means that the vertex of the parabola is (-4, 0).
By looking at the graph provided, it can be seen that the vertex of the graph is also (-4, 0). Therefore, Zander can conclude that the two functions have the same vertex.
Zander cannot conclude that they have the same x-intercept or y-intercept. The x-intercepts of a quadratic function can be found by setting f(x) = 0 and solving for x. The y-intercept is found by setting x = 0.
Without additional information or equations, Zander cannot determine whether these two functions have the same x-intercept, or even if they have any x-intercepts at all. Similarly, without additional information or equations, Zander cannot determine whether the two functions have the same y-intercept.
Finally, Zander cannot conclude that the two functions have the same range. The range of a function is the set of all possible output values. The range of the function f(x) = (x + 4)2 is all non-negative real numbers. However, without additional information about the graph’s range, Zander cannot determine whether the graph represented also has the same range.
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