Answer:
y = -2x²
Explanation:
The set of ordered pairs is:
(x₁, y₁) = (2, -8)
(x₂, y₂) = (3, -18)
(x₃, y₃) = (4, -32)
(x₄, y₄) = (5, -50)
First let's check if this is linear. For even increments of x, Δy is:
Δy₂₁ = y₂ − y₁ = -18 − -8 = -10
Δy₃₂ = y₃ − y₂ = -32 − -18 = -14
Δy₄₃ = y₄ − y₃ = -50 − -32 = -18
Δy isn't constant, so this isn't linear. However, the difference of the differences is constant:
Δy₃₂ − Δy₂₁ = -14 − -10 = -4
Δy₄₃ − Δy₃₂ = -18 − -14 = -4
So this is a quadratic.
y = ax² + bx + c
To find the coefficients of a, b, and c, we can either plug in three points from the set and solve the system of equations:
-8 = a(2)² + b(2) + c
-18 = a(3)² + b(3) + c
-32 = a(4)² + b(4) + c
Or, if it's simple, we can use a little trial and error.
-8 = -2 (2)²
-18 = -2 (3)²
-32 = -2 (4)²
So the function is:
y = -2x²