Question

Graph the data in the table. Which kind of function best models the data? Write an equation to model the data. quadratic; y = 2.5x2 linear; y = 2.5x quadratic; y = –2.5x2 exponential; y = 2.5x

Answer 1

Answer:

Option (1)

Step-by-step explanation:

x               -2              -1                 0                    1                   2

y               10            2.5                0                  2.5                3.0

Ist difference,

$d_1=y_2-y_1$

    $=2.5-10=-7.5$

$d_2=y_3-y_2$

    $=0-2.5$

    = -2.5

$d_3=y_4-y_3$

    $=2.5-0$

    = 2.5

$d_4=y_5-y_4$

    $=10.0-2.5$

    = 7.5

2nd difference,

$x_1=d_2-d_1$

    $=-2.5+7.5$

    = 5

$x_2=d_3-d_2$

    $=2.5+2.5$

    = 5

$x_3=d_4-d_3$

    $=7.5-2.5$

    = 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.