First write the function in vertex form. Then find the function information below. ​(A) Intercepts ​(B) Vertex ​(C) Maximum or minimum ​(D) Range ​g(x)equals0.25 x squared minus 1.5 x minus 8 Question content area bottom Part 1 Choose the correct vertex form below. A.g left parenthesis x right parenthesis equals 0.25 left parenthesis x minus 3 right parenthesis squared minus 8 g left parenthesis x right parenthesis equals 0.25 left parenthesis x minus 3 right parenthesis squared minus 8 B.g left parenthesis x right parenthesis equals 0.25 left parenthesis x minus 0.75 right parenthesis squared minus 8 g left parenthesis x right parenthesis equals 0.25 left parenthesis x minus 0.75 right parenthesis squared minus 8 C.g left parenthesis x right parenthesis equals 0.25 left parenthesis x minus 0.75 right parenthesis squared minus 10.25 g left parenthesis x right parenthesis equals 0.25 left parenthesis x minus 0.75 right parenthesis squared minus 10.25 D.g left parenthesis x right parenthesis equals 0.25 left parenthesis x minus 3 right parenthesis squared minus 10.25 g left parenthesis x right parenthesis equals 0.25 left parenthesis x minus 3 right parenthesis squared minus 10.25

The vertex form of a quadratic function is given by g(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.

Given the function g(x) = 0.25x² - 1.5x - 8, we can convert it to vertex form by completing the square.

First, factor out the coefficient of x² from the first two terms:

g(x) = 0.25(x² - 6x) - 8

Next, to complete the square, we take half of the coefficient of x, square it, and add and subtract it inside the parenthesis:

g(x) = 0.25(x² - 6x + 9 - 9) - 8 = 0.25[(x - 3)² - 9] - 8 = 0.25(x - 3)² - 0.25*9 - 8 = 0.25(x - 3)² - 2.25 - 8 = 0.25(x - 3)² - 10.25

So, the correct vertex form is:

g(x) = 0.25(x - 3)² - 10.25

Therefore, the correct answer is D. g(x) = 0.25(x - 3)² - 10.25

Now, let's find the function information:

(A) Intercepts: The x-intercepts are the values of x for which g(x) = 0. To find them, set the function equal to zero and solve for x:

0.25(x - 3)² - 10.25 = 0 (x - 3)² = 41 x = 3 ± √41

The y-intercept is the value of g(x) when x = 0, which is -8.

(B) Vertex: The vertex of the function is given by (h, k), which is (3, -10.25).

(C) Maximum or minimum: Since the coefficient of x² is positive, the parabola opens upwards, so the function has a minimum at the vertex.

(D) Range: Since the function has a minimum, the range is all values greater than or equal to the y-coordinate of the vertex, which is [-10.25, ∞).