Question

Dana kicks a soccer ball. The table shows the height of the soccer ball with respect to the time, in seconds, after the ball was kicked.

Time | Height
(Seconds) | (Feet)
~~~~~~~~~~~~~~~
0.5 21
1 34
1.5 39
2 36
2.5 25
3 6

Which Graph best displays the relationship shown in the table?

(i just need confirmation that its C)
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Answer 1

Answer: It is!!!!!!!!

Answer 2

The correct option is C.

Explanation:

The standard form of a parabola is

`y=ax^2+bx+c`

The table of values represents the coordinate pairs of the parabola. It means the graph of the parabola must be passes through these coordinate pairs.

From the given table it is clear that the parabola passes through the points (0.5,21), (1,34) and (1.5,39).

`21=a(0.5)^2+b(0.5)+c`

`21=0.25a+0.5b+c` .... (1)

`34=a(1)^2+b(1)+c`

`34=a+b+c` .... (2)

`39=x(1.5)^2+y(1.5)+z`

`39=2.15a+1.5b+c` .... (3)

On solving (1), (2) and (3), we get

`a=-16, b=50,c=0`

The equation of parabola is

`y=-16x^2+50x+0`

`y=-16x^2+50x`

The graph of parabola is shown below. It is same as graph in option C.

Therefore the correct option is C.