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Write an equation for the graph (image)

Write an equation for the graph (image)-example-1

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Answer:

y = -2x² + 12x - 16

Explanation:

The graph appears to be an inverted parabola.

The equation of a parabola is

y = ax² + bx + c

Use point (3, 2).

2 = a(3²) + b(3) + c

9a + 3b + c = 2 Eq. 1

Use point (2, 0).

0 = a(2²) + b(2) + c

4a + 2b + c = 0 Eq. 2

Use point (4, 0).

0 = a(4²) + b(4) + c

16a + 4b + c = 0 Eq. 3

We have a system of three equations in three unknowns, a, b, and c.

9a + 3b + c = 2

4a + 2b + c = 0

16a + 4b + c = 0

Subtract Eq. 2 from Eq. 1.

Subtract Eq. 2 from Eq. 3

5a + b = 2

12a + 2b = 0

-10a - 2b = -4

(+) 12a + 2b = 0

-----------------------------

2a = -4

a = -2

5(-2) + b = 2

b = 12

9a + 3b + c = 2

-18 + 36 + c = 2

c = -16

y = -2x² + 12x - 16

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