Question

Determine whether the graph of y = x2 + 2x − 8 has a maximum or minimum point, then find the maximum or minimum value.
A. Maximum; −9
B. Minimum; −9
C. Maximum; −1
D. Minimum; −1

Answer 1

Since this is a parabola and the x^2 coefficient is positive, the graph opens up and, hence, has a minimum point at its vertex.

Then, by completing the square, we see that:
y = x^2 + 2x - 8 = (x^2 + 2x + 1) - 9 = (x + 1)^2 - 9.

By comparing this to vertex form, y = a(x - h)^2 + k, which has its vertex at (h, k), we see that the vertex is located at (-1, -9).

Therefore, the answer is (B) Minimum; (-1, -9).

Answer 2

B. Minimum; −9

Answer 3

The parablola opens upward and has a minimum at its vertex. The x coordinate of the vetex is -b/2a which is -1 which when evaluated by the function yields -9.