Respuesta :

mreijepatmat
y = ax² + bx + c 
We have to calculate a, b and c from the given table

1st Calculate c:
for x = o, y = -1.55 
- 1.55 = a(0)² + b(0) + c → then c = -1.55
and the equation becomes: y = ax² + b.x - 1.55

2nd Calculate a and b:
for x = 2 , y = 17.29
17.29 =a(2)² + b(2) - 1.55 → 4a + 2b - 1.55 = 17.29 or 4a + 2b = 18.84 (1)

for x = 4 , y = 54.93
54.93=a(4)² + b(4) - 1.55 → 16a + 4b - 1.55 = 54.93 or 16a + 4b = 56.48 (2)

Now solve the system of 2 equations:
4a + 2b = 18.84 (1)
16a + 4b = 56.48 (2)

And you will find :

a= 2.35   and b = 4.72 . And the final equation is:

y = 2.35.x² + 4.72x - 1.55

MrRoyal

The quadratic equation defined by the table is f(x) = 2.35x^2 + 4.72x -1.55

How to determine the function?

A quadratic function is represented as:

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

Using the table of values, we have:

a(0)^2 + b(0) + c = -1.55

This gives

c = -1.55

Also, we have:

a(2)^2 + b(2) + c = 17.29

4a + 2b -1.55 = 17.29

This gives

4a + 2b = 18.84

Divide through by 2

2a + b = 9.42 --- (2)

Also, we have:

a(4)^2 + b(4) + c = 54.93

16a + 4b -1.55 = 54.93

This gives

16a + 4b = 56.48

Divide through by 4

4a + b = 14.12 ---- (3)

Subtract (2) from (3)

2a = 4.7

Divide by 2

a = 2.35

Substitute a = 2.35 in 4a + b = 14.12

4*2.35 + b = 14.12

Evaluate

b = 4.72

Substitute values for a, b and c in f(x) = ax^2 + bx + c

f(x) = 2.35x^2 + 4.72x -1.55

Hence, the quadratic equation defined by the table is f(x) = 2.35x^2 + 4.72x -1.55

Read more about quadratic equation at:

https://brainly.com/question/1214333

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