Which is the graph of the function f(x) = x2 + 2x + 3?

Mathematics

2 answers:

andrezito [222]4 years ago

8 0

Its the first answer on e2020 :D

blagie [28]4 years ago

5 0

Dy/dx=2x+2

So velocity will be zero when 2x+2=0, x=-1

Since d2y/dx2=2, it has a constant positive acceleration of 2, so that when dy/dx=0 it is at an absolute minimum value for f(x), which is also the vertex.

y(-1)=1-2+3=2

So the vertex is at (-1,2), which is an absolute minimum so the parabola opens upwards.

And by symmetry we can say that f(0)=f(-2)=3 so you have another two points that you can see (-2,3) and (0,3)

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Which type of conic section is described by the following equation?

krok68 [10]

Answer:

C. Hyperbola opening up and down

Step-by-step explanation:

A graph tells the tale.

___

The term with the positive coefficient identifies the axis along which the hyperbola opens. Here, that is the y-axis, so the figure opens up and down.

The minus sign between the squared terms indicates it is a hyperbola, rather than a closed curve (ellipse or circle). The fact that both terms are squared indicates it is <em>not</em> a parabola.