Which is the graph of the function f(x) = x2 + 2x + 3?
2 answers:
Answer:
Refer the graph attached.
Step-by-step explanation:
Given : Equation
To find : The graph of the given equation?
Solution :
Let,
First we find the points which satisfy the equation and then joining those points give you the graph.
Points are
x y
-3 6
-2 3
-1 2
0 3
1 6
Now, We plot these points.
The graph is the parabola with vertex (-1,2).
Refer the attached graph below.
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Let's write the general form of the sine curve:
, where,
- A is the amplitude. Also, if A is negative, curve reflects about x axis
- B is the compression/stretching factor. It changes the period when it is a value other than 1.
- C is the phase shift. It translates curve left or right. Negative value shifts right and positive value shifts left.
- D is the vertical shift. It translates curve up or down. Negative value shifts down and positive value shifts up.
Let's check the 4 choices.
A.
Since this curve's A is -2, its amplitude is 2 and range is from -2 to 2. BUT since D value is -3, it shifts vertically 3 units down making the range from -1 to -5. Clearly choice A is not true.
B.
This graph is the graph of shifted 3 units DOWN since D is negative. This choice isn't true.
C.
Because of the - (minus) sign in front of the function, the function is reflected about x-axis, but amplitude doesn't change. Since A value is 2, amplitude is 2. This is true.
D.
Period depends on the B value. Here, B value is 1, so period is normal as the parent function of a sine curve, which is , NOT
. So this is not correct.
ANSWER: C is true