Question
How does the graph of g(x) = x2+3 compare to that of f(x) = x2
Hint:
The vertex form of a quadratic function is
f(x) = a(x – h)2 + k
Where a, h, and k are constants. Here, h represents horizontal translation, a represents vertical translation and (h, k) is the vertex of the parabola. Also, a represents the Vertical stretch/shrink of the parabola and if a is negative, then the graph is reflected over the x-axis.
The correct answer is: Hence, g(x) is 3 units up from f(x).
The parent function is:
f(x) = x2
In this problem, g(x)= x2 + 3 so if f(x) was shifted 3 units up, the value of f(x) will be
f(x) = x2 + 3 = g(x)
So, g(x) is 3 units up from f(x)
Final Answer:
Hence, g(x) is 3 units up from f(x).
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