Answer:
3.5
Step-by-step explanation:
Answer:
The equation of the parabola is 
, whose real vertex is 
, not 
.
Step-by-step explanation:
A parabola is a second order polynomial. By Fundamental Theorem of Algebra we know that a second order polynomial can be formed when three distinct points are known. From statement we have the following information:
, 
, 
From definition of second order polynomial and the three points described above, we have the following system of linear equations:
(1)
(2)
(3)
The solution of this system is: 
, 
, . Hence, the equation of the parabola is . Lastly, we must check if belongs to the function. If we know that 
, then the value of 
is:
does not belong to the function, the real point is .
Important: Please use " ^ " to indicate exponentiation:
<span>"f(x) =x^2 to the number of x-intercepts in the graph of g(x) = x^2 +2."
Notes: the graph of f(x) = x^2 is a vertical parabola that opens up. It has its vertex at (0,0). This is the only point at which f(x)=x^2 has a horiz. intercept.
g(x) = x^2 + 2 has a graph that looks the same as that of f(x) = x^2, EXCEPT that the whole graph is moved 2 units UP. This new graph never touches or intersects the x-axis. Therefore, g(x) has NO horiz. intercepts (no x-int.).
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