Graph the function y=|x+2|-3
2 answers:
Answer:
The graph has been attached.
Step-by-step explanation:
We have to graph the function y=|x+2|-3
The parent function is y = |x|.
It is a v-shaped curve, with vertex at (0,0) as shown in the figure with dotted curve.
We use rule of transformation of graph:
- When we add a constant 'a' in x then graph shifts 'a' units left
- When we subtract a constant 'a' in function then graph shifts a units down
Now, we translate this graph 3 units down and 2 units left. Thus, the equation of the parent function becomes y=|x+2|-3. The curve is v-shaped and the vertex is at (-2,-3).
Now, we can easily graph the function y=|x+2|-3
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here.
Step-by-step explanation:
Since you need the vertex, and knowing the vertex will tell you the axis of symmetry, it is convenient to put the equation in vertex form.
.. -x^2 -4x +1
.. = -(x^2 +4x) +1
.. = -(x^2 +4x +(4/2)^2) +1 -(-(4/2)^2) . . . . complete the square
.. = -(x +2)^2 +5
The vertex is (-2, 5).
The axis of symmetry is x = -2.
.. -x^2 -4x +1
.. = -(x^2 +4x) +1
.. = -(x^2 +4x +(4/2)^2) +1 -(-(4/2)^2) . . . . complete the square
.. = -(x +2)^2 +5
The vertex is (-2, 5).
The axis of symmetry is x = -2.