Question

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Answer 1

Hint :- If x=a is the axis of symmetry then

f(a+h)=f(a-h)

Answer 2

To draw the graph for f(x)

f(x)=-4(x-8)^2+3=-4x^2+64x-253.
the graph will be a parabola opening downwards due to a=-4 which is less than 0.

Answer 3

maximum value of f(x)=-D/4a
where D is the discriminant.

Answer 4

use this information to draw the graph.

Also remember that the graph will intersect x-axis at the roots.