Maths-
General
Easy
Question
How does the graph of f(x) = -3(x - 5)2 + 7 compare to the graph of the parent function
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, f(x) is shafted 5 units right, stretched 3 units, reflected over x-axis and moved 7 units up from the parent function g(x) = x2.
The parent function for the quadratic function is g(x) = x2
In this problem, f(x) = -3(x - 5)2 + 7 so if g(x) was shifted 5 units right, the value of g(x) will be
g(x) = (x - 5)2
Now, stretch the new function 3 times and multiply it by -1 which will reflect the function over the x-axis. The value of g(x) will be
g(x) = -3(x - 5)2
Now, the new g(x) is moved 7 units up. So, the value of g(x) will be
g(x) = -3(x - 5)2 + 7 = f(x)
So, f(x) is shafted 5 units right, stretched 3 units, reflected over the x-axis and moved 7 units up from the parent function.
Final Answer:
Hence, f(x) is shafted 5 units right, stretched 3 units, reflected over x-axis and moved 7 units up from the parent function g(x) = x2.
Now, stretch the new function 3 times and multiply it by -1 which will reflect the function over the x-axis. The value of g(x) will be
g(x) = -3(x - 5)2
Now, the new g(x) is moved 7 units up. So, the value of g(x) will be
So, f(x) is shafted 5 units right, stretched 3 units, reflected over the x-axis and moved 7 units up from the parent function.
Final Answer:
Hence, f(x) is shafted 5 units right, stretched 3 units, reflected over x-axis and moved 7 units up from the parent function g(x) = x2.
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