Question

1.

Graph the data in the table. Which kind of function best models the data? Write an equation to model the data.

A. quadratic; y = –2.5x2

B. linear; y = 2.5x

C. exponential; y = 2.5x

D. quadratic; y = 2.5x2

Answer 1

D. quadratic; y = 2.5x2

Explanation:

Answer:

A. quadratic; y = 2.5x2

Step-by-step explanation:

Answer:

Option (1)

Step-by-step explanation:

x -2 -1 0 1 2

y 10 2.5 0 2.5 3.0

Ist difference,

= -2.5

= 2.5

= 7.5

2nd difference,

= 5

= 5

= 5

Since 2nd difference is common, given table represents a quadratic equation.

Let the equation is,

y = ax²+ bx + c

For a point (0, 0) passing through the quadratic equation,

0 = c

Therefore, quadratic equation is y = ax² + bx

Since ordered pair (-1, 2.5) passes through the graph of the function,

2.5 = a(-1)² + b(-1)

a - b = 2.5 ------(1)

For another point (1, 2.5)

2.5 = a(1)² + b(1)

a + b = 2.5 ------(2)

By adding equations (1) and (2),

2a = 5

a = 2.5

and from equation (2)→ y = 0

Therefore, equation of the quadratic function given in the table is y = 2.5x²

Option (1) is the answer.