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vivado [14]
3 years ago
15

Which is the graph of the function f(x) = x2 + 2x – 6? Mark this and return

Mathematics
2 answers:
valina [46]3 years ago
6 0
Vertex: ( -1, -7 )

Focus: ( -1, -27/4 )

Axis of Symmetry: x = -1

Directrix: y = -29/4


X | Y
———
-3| -3
-2| -6
-1 | -7
0 | -6
1 | -3

Ghella [55]3 years ago
3 0

Answer:

The graph of the function is shown below.

Step-by-step explanation:

The given function is

f(x)=x^2+2x-6

f(x)=(x^2+2x)-6

If an expression is defined as x^2+bx, then we need to add (\frac{b}{2})^2 to make it perfect square.

Here, b=2 so add and subtract 1 in the above parenthesis.

f(x)=(x^2+2x+1-1)-6

f(x)=(x^2+2x+1)-1-6

f(x)=(x+1)^2-7         .... (1)

The vertex form of a parabola is

f(x)=(x-h)^2+k      .... (2)

where, (h,k) is vertex.

On comparing (1) and (2) we get

h=-1,k=-7

So, the vertex of the parabola is (-1,-7) and axis of symmetry is x=-1.

The x-intercepts of the equation is

0=(x+1)^2-7

7=(x+1)^2

\pm \sqrt{7}=x+1

-1\pm \sqrt{7}=x

x=-3.646,1.646

Therefore, the x-intercepts are -3.646 and 1.646. The graph is shown below.

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Answer:

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Step-by-step explanation:

Let suppose that bus runs at constant speed and that speed is measured in kilometers per hour. Then, the speed of the bus (v), in kiometers per hour, is determined by following kinematic expression:

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