Answer:
Step-by-step explanation:
The graph that will lie above the x-axis will be having only positive values throughout its domain,
So, We have to check which graph is having y > 0 for every x.
clearly y will be negative for many values of x , as coefficient of variable is negative.
Put x = 0, you will get y as negative .
Since, Square of anything will always be positive , and here constant term is also positive , so, It will always be positive .
Thus, it is having its graph always above x axis.
Put x = 0 , y = -7, which is negative
Answer:
Option C.
Step-by-step explanation:
The vertex form of a parabola is
[tex]y=a(x-h)^2+k[/tex]
where, a is constant, (h,k) is vertex.
If a<0, then it is a downward parabola and if a>0, then it is an upward parabola.
A downward parabola never lies entirely above the x-axis.
First equation is
[tex]y=-(x+7)^2+7[/tex]
It is a downward parabola and vertex is (-7,7).
Second equation is
[tex]y=(x-7)^2-7[/tex]
It is an upward parabola and vertex is (7,-7).
Third equation is
[tex]y=(x-7)^2+7[/tex]
It is an upward parabola and vertex is (7,7).
Fourth equation is
[tex]y=(x-7)[/tex]
It is a linear equation with y-intercept -7.
Only equation 3 is an upward parabola whose vertex lies above the x-axis.
Hence the correct option is C.
