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If a person who is 5. 5 feet tall throws a baseball into the air, the path can be modeled using the table of values, where x represents the time in seconds and y is the height of the ball in feet.



x y

0 5. 5

1 7. 35

2 8. 9

3 10. 15

4 11. 1

5 11. 75


Which quadratic equation models the data in the table?

y= −0. 25x2 + 2x + 5. 5

y= −0. 35x2 + 2x + 5. 5

y= −0. 27x2 + 3x + 5. 5

y= −0. 15x2 + 2x + 5. 5

Respuesta :

MrRoyal

The data in the table is an illustration of a quadratic equation, and the quadratic equation that models the data is (d) y = -0.15x² + 2x + 5.5

How to determine the quadratic model?

A quadratic model is represented as:

y = ax² + bx + c

Using the point (x,y) = (0,5.5);

We have:

a(0)² + b(0) + c = 5.5

This gives

c = 5.5

Substitute c = 5.5 in y = ax² + bx + c

y = ax² + bx + 5.5

Using the point (x,y) = (1,7.35);

We have:

a(1)² + b(1) + 5.5 = 7.35

This gives

a + b + 5.5 = 7.35

Subtract 5.5 from both sides

a + b = 1.85

Using the point (x,y) = (2, 8.9);

We have:

a(2)² + b(2) + 5.5 = 8.9

This gives

4a + 2b + 5.5 = 8.9

Subtract 5.5 from both sides

4a + 2b = 3.4

Divide through by 2

2a + b = 1.7

Subtract a + b = 1.85 from 2a + b = 1.7

2a - a + b - b = 1.7 - 1.85

This gives

a = -0.15

Substitute a = -0.15 in 2a + b = 1.7

-2 * 0.15 + b = 1.7

This gives

-0.3 + b = 1.7

Add 0.3 to both sides

b = 2

Substitute a = -0.15 and b = 2 in y = ax² + bx + 5.5

y = -0.15x² + 2x + 5.5

Hence, the quadratic equation that models the data in the table is (d) y = -0.15x² + 2x + 5.5

Read more about quadratic equations at:

https://brainly.com/question/10449635

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