Pls help, thank you Find the quadratic function y = ax2+bx+c whose graph passes through the given points.
(-2,-35), (1,-5), (3,- 15)
y =

y = -3x² + 7x - 9

Step-by-step explanation:

Given quadratic function:

y = ax² + bx + c

Points on the graph:

(-2,-35), (1,-5), (3,- 15)

Substitute values of x and y and solve the system of equations:

-35 = a(-2)² + b(-2) + c ⇒ -35 = 4a - 2b + c   ⇔ eq 1-5 = a(1)² + b(1) + c ⇒ -5 = a + b + c               ⇔ eq 2-15 = a(3)² + b(3) + c ⇒ -15 = 9a + 3b + c       ⇔ eq 3

Subtract eq 2 from eq 1:

-35 - (-5) = 4a - 2b + c - a - b - c-30 = 3a - 3b b = a + 10                                                         ⇔ eq 4

Subtract eq 2 from eq 3:

-15 - (-5) = 9a + 3b + c - a - b - c-10 = 8a + 2bb = -4a - 5                                                       ⇔ eq 5

Compare eq 4 and eq 5, solve for a:

a + 10 = -4a - 5a + 4a = -5 - 105a = -15a = -3

Find the value of b using eq 4:

b = -3 + 10b = 7

Find the value of c using eq 2:

-5 = -3 + 7 + cc = -5 - 4c = -9

We now have a, b and c:, the function is:

y = -3x² + 7x - 9