Please help please and thanks

A

Step-by-step explanation:

Using the standard form of the parabola , y = ax² + bx + c ( a ≠ 0 )

Substitute the given points into the equation and solve for a, b, c using simultaneous equations.

(- 5, 10 )

- 10 = a(- 5)² - 5b + c, that is

25a - 5b + c = - 10 → (1)

(- 3, 2 )

2 = a(- 3)² - 3b + c, that is

9a - 3b + c = 2 → (2)

(2, - 3 )

- 3 = a(2)² + 2b + c , that is

4a + 2b + c = - 3 → (3)

Eliminate c from the equations

Subtract (2) from (1) term by term

16a - 2b = - 12 → (4)

Subtract (3) from (2) term by term

5a - 5b = 5 → (5)

Multiply (4) by 5 and (5) by - 2 then add to eliminate b

80a - 10b = - 60 → (6)

- 10a + 10b = - 10 → (7)

Add (6) and (7) term by term

70a = - 70 ( divide both sides by 70 )

a = - 1

Substitute a = - 1 into (4) and evaluate for b

- 16 - 2b = - 12 ( add 16 to both sides )

- 2b = 4 ( divide both sides by - 2 )

b = - 2

Substitute a = - 1, b = - 2 into (3) and evaluate for c

- 4 - 4 + c = - 3

- 8 + c = - 3 ( add 8 to both sides )

c = 5

Thus a = - 1, b = - 2 and c = 5

Substitute these values into the standard parabola, that is

y = - x² - 2x + 5 → A