Which function has the greater maximum value f(x)=-2x^2+4x+3 or g(x), the function in the graph?

A

Step-by-step explanation:

Alright so in the graph we can see the highest y that is reach is at x=3 which is y=6.  The maximum of the graph g(x) is 6.

Now we have to be a bit more algebraic and messy when comes to finding a maximum (the vertex of the parabola) of f(x)=-2x^2+4x+3.

First step, I'm going to find the x-coordinate of the vertex.  Once we do that we can find the y that corresponds to it by using y=-2x^2+4x+3.

So the x-coordinate of the vertex can be found by computing -b/(2a).

a=-2 and b=4 so we are going to plug that in giving us -4/(2*-2)=-4/-4=1.

So the x-coordinate of the vertex is 1 and we are going to find the y that corresponds to that using y=-2x^2+4x+3.

So let's plug in 1.

This gives us:

y=-2(1)^2+4(1)+3

y=-2(1)+4+3

y=-2+4+3

y=2+3

y=5

So the maximum of graph f is 5.

6 is higher than 5

So g has the higher maximum

So the answer is A.

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