Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your work.

Solution:

The standard form of a quadratic equation is y = ax² + bx + c

There are 3 unknown coefficients a, b, and c, and 2 variables x and y

By substituting the given 3 points (-2, -20), (0, -4), (4, -20), let us find 3 equations.

-20 = a(-2)² + b(-2) + c

-4 = a(0)² + b(0) + c

-20 = a(4)² + b(4) + c

By simplification

-20 = 4a - 2b + c -----> (1)

c = -4 -----> (2)

-20 = 16a + 4b + c ----->(3)

Subtracting equation (3) by (1)

-20 = 16a + 4b + c
-20 = 4a - 2b + c
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0 = 12a + 6b + 0

So we get,

6b= -12a

b = -2a --- (4)

Substituting the value of b and c in equation (1)

-20 = 4a - 2 (-2a) - 4

-20 = 4a + 4a - 4

-16 = 8a

a = -2

Substituting it in equation (4)

b = -2(-2) = 4

So the model is

y = -2x² + 4x - 4

Therefore, the quadratic model is y = -2x² + 4x - 4.

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Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your work.

Summary:

A quadratic model for the set of values (-2, -20), (0, -4), (4, -20) is y = -2x² + 4x - 4.