Write a function to represent the set of ordered pairs. {(2, -8), (3, -18), (4, -32), (5, -50)}

y = -2x²

Step-by-step 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

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.