Answer:
Option (1)
Step-by-step explanation:
x -2 -1 0 1 2
y 10 2.5 0 2.5 3.0
Ist difference,
[tex]d_1=y_2-y_1[/tex]
[tex]=2.5-10=-7.5[/tex]
[tex]d_2=y_3-y_2[/tex]
[tex]=0-2.5[/tex]
= -2.5
[tex]d_3=y_4-y_3[/tex]
[tex]=2.5-0[/tex]
= 2.5
[tex]d_4=y_5-y_4[/tex]
[tex]=10.0-2.5[/tex]
= 7.5
2nd difference,
[tex]x_1=d_2-d_1[/tex]
[tex]=-2.5+7.5[/tex]
= 5
[tex]x_2=d_3-d_2[/tex]
[tex]=2.5+2.5[/tex]
= 5
[tex]x_3=d_4-d_3[/tex]
[tex]=7.5-2.5[/tex]
= 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.
