Answer:
see below
Step-by-step explanation:
f(x) = −16x^2 + 24x + 16
Set equal to zero to find the x intercepts
0 = −16x^2 + 24x + 16
Factor out -8
0 = -8(2x^2 -3x-2)
Factor
0 = -8(2x +1) (x-2)
Using the zero product property
2x+1 =0 x-2 =0
x = -1/2 x=2
The x intercepts are -1/2 ,2
Since the coefficient of x^2 is negative the graph will open down and the vertex will be a maximum
The x value of the maximum is 1/2 way between the zeros
(-1/2+2) /2 = 1.5/2 =.75
To find the y value substitute into the function
f(.75) = -8(2x +1) (x-2)
=-8(2*.75+1) (.75-2)
= -8(2.5)(-1.25)
=25
The vertex is at (.75, 25)
We have the zeros, and the vertex. We know the graph is symmetrical about the vertex
I think it's the 2 one I'm 76 percent sure
1. It is a triangular prism
By definition, we have
So, we have to solve two different equations, depending of the possible range for the variable. We have to remember about these ranges when we decide to accept or discard the solutions:
Suppose that 
In this case, the absolute value doesn't do anything: the equation is
We are supposing 
, so we can accept this solution.
Now, suppose that 
. Now the sign of the expression is flipped by the absolute value, and the equation becomes
Again, the solution is coherent with the assumption, so we can accept this value as well.
You can give random values such as <span> (1,2.5) (2,9) (-1,2.5) (-2,9) and it is a parabola. You'll see that the range is (-infinte, 0] and the domain is (-infinit, infinite). </span>I hope that this is the answer that you were looking for and it has helped you.
