Question

The following scatter plot represents the height of a basketball in seconds during a free throw shot.

Answer 1

The function is not treated as linear because whenever we throw the thing in the air it traces the path of the parabola which is quadratic. Then the quadratic equation is y = -1.25x² + 7.35x + 3.2.

What is a quadratic equation?

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

The following scatter plot represents the height of a basketball in seconds during a free throw shot.

(a) A student chose to model the data with the function, y = 0.9286x + 9.0571 . Then the function is not treated as linear because whenever we throw the thing in the air it traces the path of the parabola which is quadratic.

(b) Write a function

We know that the quadratic equation is given as ax² + bx + c = y

This will pass through the points (1, 9.3), (2, 12.9), and (3, 14). Then we have

$\rm a + b + c = 9.3 \ \ \ \ \ \ \ ...1\\\\4a + 2b + c = 12.9 \ \ \ ...2\\\\9a + 3b + c = 14 \ \ \ \ \ \ ...3$

On solving the equations 1, 2, and 3. Then we have

a = -1.25, b = 7.35, and c = 3.2

Then the quadratic equation will be

y = -1.25x² + 7.35x + 3.2

More about the quadratic equation link is given below.

brainly.com/question/2263981

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