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Step-by-step explanation:

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-16x^2 + 24x + 16 = 0.

A. Divide by 8:

-2x^2 + 3x + 2 = 0, A*C = -2*2 = -4 = -1 * 4. Sum = -1 + 4 = 3 = B, -2x^2 + (-x+4x) + 2 = 0,

(-2x^2-x) + (4x+2) = 0,

-x(2x+1) + 2(2x+1) = 0,

(2x+1)(-x+2) = 0, 2x+1 = 0, X = -1/2. -x+2 = 0, X = 2.

X-intercepts: (-1/2,0), (2,0).

B. Since the coefficient of x^2 is negative, the parabola opens downward. Therefore, the vertex is a maximum.

Locate the vertex: h = Xv = -B/2A = -24/-32 = 3/4, Plug 3/4 into the given Eq to find k(Yv). K = -16(3/4)^2 + 16(3/4) + 16 = 19. V(h,k) = V(3/4,19).

C. Choose 3 points above and below the vertex for graphing. Include the points calculated in part A which shows where the graph crosses the x-axis.