Answer:
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 + 2b
b = -4a - 5 ⇔ eq 5
Compare eq 4 and eq 5, solve for a:
a + 10 = -4a - 5
a + 4a = -5 - 10
5a = -15
a = -3
Find the value of b using eq 4:
b = -3 + 10
b = 7
Find the value of c using eq 2:
-5 = -3 + 7 + c
c = -5 - 4
c = -9
We now have a, b and c:, the function is:
y = -3x² + 7x - 9
