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The graph of a quadratic function is a parabola that opens down and has a vertex of (4, 3). Which of the following could be the function?

A.
y=-x^2+4x+3
B.
y=-x^2+8x-13
C.
y=x^2-4x+3
D.
y=x^2-8x-13

Respuesta :

irspow
If the vertex is at the maximum point they dy/dx=0 at that point...

dA/dx=-2x+4

dB/dx=-2x+8

dC/dx=2x-4

dD/dx=2x-8

So both B and D have a zero velocity at x=4, but only B is equal to 3 when x=4

B. is the correct quadratic with the vertex at (4,3)

Answer:

B.

 [tex]y=-x^{2} +8x-13[/tex]

Step-by-step explanation:

We know that the vertex of the parabola is

[tex]V(4,3)[/tex]

That means this points is being intercept by the parabola. In other words, the function that represents this parabola has to have this relation, when [tex]x=4[/tex], [tex]y=3[/tex].

So, you can observe that the second choice has a function that follows this relation. Let's see

[tex]y=-x^{2} +8x-13[/tex]

So, for [tex]x=4[/tex]

[tex]y=-(4)^{2} +8(4)-13\\y=-16+32-13\\y=3[/tex]

Therefore, function B is the answer because it includes the vertex at its relation.

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