The table below shows the approximate height of a ball thrown up in the air after x seconds. A 2-column table with 5 rows. The first column is labeled time (seconds) with entries 0, 1, 2, 3, 4. The second column is labeled height (feet) with entries 5, 90, 140, 160, 150. Which quadratic model best represents the data? f(x) = –16x2 + 99x + 6 f(x) = –36x2 + 37x + 5 f(x) = 36x2 + 37x + 5 f(x) = 16x2 + 99x + 6

Answer:

A) . f(x) = –16x2 + 99x + 6  

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Step-by-step explanation:

By analyzing the data and the situation modeled, we got the vertex of the quadratic function, and with that, we conclude that the correct option is:

f(x) = –16x^2 + 99x + 6

Here we have the table:

x         y

0        5

1         90

2        140

3         160

4         150

First, we know that this represents the height of a ball that is thrown in the air, and we know that it must go up and then back, this means that the leading coefficient must be negative.

So there are two options:

f(x) = –16x^2 + 99x + 6

f(x) = –36x^2 + 37x + 5

Analyzing the data, we can see that the maximum value is at x = 3, so we can assume that the vertex is near x = 3.

Remember that for a quadratic:

y = a*x^2 + b*x + c

The x-value of the vertex is at:

x = -b/2a

Then for our functions the x-values of the vertex are:

f(x) = –16x^2 + 99x + 6

x = -99/(2*-16) = 3.1

f(x) = –36x^2 + 37x + 5

x = -37/(2*-36) = 0.5

The option that has a vertex near x = 3 is the first one, so that is the best fit.

f(x) = –16x^2 + 99x + 6

If you want to learn more about quadratic equations, you can read:

https://brainly.com/question/1214333

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