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puteri [66]
4 years ago
7

A parabola passes through the points (-2,8), (0,2), and (1,5). What function does the graph represent?

Mathematics
1 answer:
zheka24 [161]4 years ago
5 0

ANSWER

y = 2 {x}^{2}  + x + 2

EXPLANATION

Let the function that represent the graph be:

y = a {x}^{2}  + bx + c

The parabola passes through the points (-2,8), (0,2), and (1,5).

These points must satisfy the function.

For (-2,8), we have

8= a{( - 2)}^{2}  + b( - 2) + c

This implies that that,

4a - 2b + c = 8...(1)

For (0,2), we have,

2= a{( 0)}^{2}  + b( 0) + c

This implies that,

c = 2

For (1,5), we have

5= a{( 1)}^{2}  + b( 1) + c

This implies that,

a + b + c = 5...(2)

Put c=2 into equation (1) and (2).

4a - 2b + 2 = 8

4a - 2b  = 8 - 2

4a - 2b = 6

2a - b = 3...(3)

a + b + 2=5

a + b =5 - 2

a + b = 3...(4)

Add equation (3) and equation (4)

3a = 6

a = 2

Put a=2 into equation (4).

2 + b = 3

b = 3 - 2 = 1

Therefore the function is

y = 2 {x}^{2}  + x + 2

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