Question

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) = â€"16x2 99x 6 f(x) = â€"36x2 37x 5 f(x) = 36x2 37x 5 f(x) = 16x2 99x 6.

Answer 1

The equation of the quadratic model is $f(x) = -16x^2 + 99x+ 6$

A quadratic regression equation is represented as:

$f(x) =ax^2 + bx + c$

Where:

$a = \frac{ [ \sum x^2 y * \sum xx ] - [\sum xy * \sum xx^2 ] }{ [ \sum xx * \sum x^2x^2] - [\sum xx^2 ]^2 }$

$b = \frac{ [ \sum xy * \sum x^2x^2 ] - [\sum x^2y * \sum xx^2 ] }{ [ \sum xx * \sum x^2x^2] - [\sum xx^2 ]^2 }$

$c = [ \frac{\sum y }{ n} ] - { b \times [ \frac{\sum x }{ n} ] } - { a * [ \frac{\sum x^2}{ n} ] }$

Using a graphing calculator, we have:

$a = -15.714$

$b= 98.857$

$c = 5.571$

Approximate to the nearest integers

$a = -16$

$b = 99$

$c = 6$

Substitute these values in $f(x) =ax^2 + bx + c$

$f(x) = -16x^2 + 99x+ 6$

Hence, the equation of the quadratic model is $f(x) = -16x^2 + 99x+ 6$

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Answer 2

Answer:

The equation of the quadratic model is

A quadratic regression equation is represented as:

Where:

Using a graphing calculator, we have:

Approximate to the nearest integers

Substitute these values in

Hence, the equation of the quadratic model is

Read more about quadratic regression models at:

brainly.com/question/25794160

Step-by-step explanation: