Maths-
General
Easy
Question
The graph of h is the graph of g(x)= (x-2)2+6 translated 5 units left and 3 units down.
a. Describe the graph of h as a translation of the graph of f(x)= x2
b. Write the function h in vertex form.
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: a) Hence, h(x) is 3 units left and 3 units up of f(x) b) The vertex form of h(x) is (x+3)2+3.
Given g(x)= (x-2)2+6
To get h(x), first g(x) is translated 5 units left
So, h(x) = (x-2+5)2+6 = (x+3)2+6
Now, g(x) is translated 3 units down
So, h(x) = (x+3)2+6 -3 = (x+3)2+3
Given f(x) = x2 and h(x) = (x+3)2+3
Now, if f(x) is translated 3 units left and 3 units up, then the value of f(x) is
f(x) = (x+3)2+3 = h(x)
So, h(x) is 3 units left and 3 units up of f(x)
Final Answer:
a) Hence, h(x) is 3 units left and 3 units up of f(x)
b) The vertex form of h(x) is (x+3)2+3.
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