The graph of this function is shifted downwards and the axis of symmetry remains x=1. which function below the equation of the new graph select all correct answer

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

where

(h,k) is the vertex

The axis of symmetry is equal to the x-coordinate of the vertex

so

If a> 0 then the parabola open upward (vertex is a minimum)

If a< 0 then the parabola open downward (vertex is a maximum)

In this problem we have

The vertex is the point ------> observing the graph

The axis of symmetry is

If the graph of this function is shifted downwards and the axis of symmetry remains x=1

then

The x-coordinate of the vertex of the new graph must be equal to 1

The y-coordinate of the vertex of the new graph must be less than 4

The parabola of the new graph open downward

therefore

Verify each case

case a)

Convert to vertex form

The vertex is (1,1)

therefore

The function could be the equation of the new graph

case b)

Convert to vertex form

The vertex is (-1,4)

therefore

The function cannot be the equation of the new graph

case c)

Convert to vertex form

The vertex is (1,-3)

therefore

The function could be the equation of the new graph

case d)

Convert to vertex form

The vertex is (1,5)

therefore

The function cannot be the equation of the new graph

case e)

Convert to vertex form

The vertex is (1,-2)

therefore

The function could be the equation of the new graph

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