Consider g (x) = - x^2 + 12x - 32 Part A: Write g (x) in vertex form, identify the vertex, and determine the x-intercepts.

(x - 6) ² = - (y - 4)

The vertex of the parabola will be (6,4).

The x-intercepts are at (8,0) and (4,0).

Step-by-step explanation:

Given the equation of parabola is g (x) = y = - x² + 12x - 32 ... (1)

Now, converting the equation to vertex form.

Here, y = - x² + 12x - 32

⇒ y = - (x² - 12x + 36) + 4

⇒ y - 4 = - (x - 6) ²

⇒ (x - 6) ² = - (y - 4) ... (2) (Answer)

Now, the vertex of the parabola will be (6,4) and it opens down. (Answer)

Let the x-intercept of the parabola is at (h, 0).

Hence, from equation (2) we get,

(h - 6) ² = - (0 - 4) = 4

⇒ h - 6 = ± 2

⇒ h = 8 or h = 4

Therefore, the x-intercepts are at (8,0) and (4,0). (Answer)