Question

Give the coordinate of the vertex without any spaces. Show the work for how you got the y-value.

The equation is: y = (1/2)(x + 4)(x - 2)
A. Vertex: (-4, 2)
B. Vertex: (-2, 4)
C. Vertex: (4, -2)
D. Vertex: (2, -4)

Answer 1

The vertex of the quadratic function y = (1/2)(x + 4)(x - 2) is found by averaging the roots for the x-value, which is (-1), and then substituting it back into the function to find the y-value (-4.5). The correct vertex is (-1, -4.5).

Step-by-step explanation:

To find the coordinate of the vertex of the quadratic function y = (1/2)(x + 4)(x - 2), we first need to find the x-value of the vertex. This will be the average of the x-values where the function crosses the x-axis (the roots).

The roots are x = -4 and x = 2, so the x-value of the vertex is (-4 + 2)/2 = -1. Now, we need to find the y-value by substituting x = -1 into the function:

y = (1/2)(-1 + 4)(-1 - 2) = (1/2)(3)(-3) = -4.5

Therefore, the coordinates of the vertex are (-1, -4.5). Since this pair is not listed in the options given, it's possible there is a typo in the question, or the answer choices provided are incorrect.