Maths-
General
Easy
Question
To graph the function f(x)= (x-5)2 -8, a student translates the graph of the quadratic parent function 5 units right and 8 units down. Can a student produce the graph of f(x)= 2(x+3)2 -5 by simply translating the quadratic parent function? Explain
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, the graph of f(x)= 2(x+3)2 -5 can be produced by simply translating the quadratic parent function.
Given f(x) = (x-5)2 -8
The parent function for the quadratic function is g(x) = x2
It is given that the quadratic parent function is 5 units right. So, f(x) becomes
g(x) = (x - 5)2
Now, the quadratic parent function is 8 units down. So, f(x) becomes
g(x) = (x - 5)2 - 8 = f(x)
Final Answer:
Hence, the graph of f(x)= 2(x+3)2 -5 can be produced by simply translating the quadratic parent function.
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