What is the range of the function y=4x^2+2?

2 Answers
Daniel L.
May 8, 2018

See explanation.

Explanation:

Graph of this function is a parabola with vertex at (0,2). The function's values go to +oo if x goes to either -oo or +oo, so the range is:

r=(2,+oo)

The graph is:

graph{4x^2+2 [-10, 10, -5, 5]}

Alan N.
May 8, 2018

Range: [+2,+oo)

Explanation:

y = 4x^2+2

y is a quadratic function of the form ax^2+bx+c
Where: a=+4,b=0 and c=+2

y will have a parabolic graph with axis of symmetry where x=-b/(2a)

:. x=0

Since a>0 y will have a minimum value at x=0

:. y_min = +2

Since, y has no finite upper bound the range of y is [+2,+oo)

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