<span>Discriminant is 28 (c)
First get the equation into the form: Ax^2 + Bx + C = 0 (the quadratic equation)..
By subtracting 10x both sides (to get it on the other side)..
9x^2 + 2 = 10x
9x^2 - 10x + 2 = 10x - 10x
9x^2 - 10x + 2 = 0
Now the discriminant is: b^2 - 4ac
The quadratic equation is Ax^2 + Bx + C = 0
Here, A = 9, B = -10 and C = 2
(-10)^2 - 4 (9)(2)
= 100 - 4 (18)
= 100 - 72
= 28</span>
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
<u>Verify each case</u>
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
Answer:
11.0905365064
11.1 (rounded)
Step-by-step explanation:
