SOLUTION: if f(x)= 3x^2, what are all real values of a and b for which the graph of g(x)= ax^2+b os below the graph of f(x) for all values of x

Question 1078221: if f(x)= 3x^2, what are all real values of a and b for which the graph of g(x)= ax^2+b os below the graph of f(x) for all values of x
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
if f(x)= 3x^2, what are all real values of a and b for which the graph of g(x)= ax^2+b is below the graph of f(x) for all values of x
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Since the vertex of f(x) is (0,0) and f(x) opens upward,
a must be negative to force g(x) to open down,
and b must be negative to assure the vertex is below (0,0)
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Cheers,
Stan H.
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Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

For to be below the graph of , must be "bigger" than .
is below the graph of if and it will be for any ( is any negative number)
and is below the graph of if , multiplying by negative number will flip it upside down AND stretch it in the y-direction
so, answer is: for any , and for any
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