Maths-
General
Easy
Question
How are the form and graph of f(x)= (x-h)2+k similar to the form and graph of f(x)=|x-h|+k? How are they different?
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)= (x-h)2+k is (h, k) and f(x)=|x-h|+k will have same vertex i.e. (h, k) and they have different shapes of graph.
The vertex of the graph of f(x)= (x-h)2+k is (h, k) and also the vertex of the graph of f(x)=|x-h|+k is (h, k)
So, f(x)= (x-h)2+k is (h, k) and f(x)=|x-h|+k will have same vertex i.e. (h, k)
Now, the graph of f(x)= (x-h)2+k is a parabola while the graph of f(x)=|x-h|+k is a V-shape graph.
Final Answer:
Hence, f(x)= (x-h)2+k is (h, k) and f(x)=|x-h|+k will have same vertex i.e. (h, k) and they have different shapes of graph.
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