Respuesta :
Answer:
(1) B
(2) D
Step-by-step explanation:
(1)
Let the quadratic function be:
[tex]y = ax^{2} + bx + c[/tex]
For the point, (0,-1),
[tex]y = ax^{2} + bx + c[/tex]
[tex]-1=(a\times0)+(b\times0}+c\\-1=c\\c=-1[/tex]
Then the equation is:
[tex]y = ax^{2} + bx -1[/tex]
For the point (-1, -8) ,
[tex]y = ax^{2} + bx -1[/tex]
[tex]-8=(a\times (-1)^{2})+(b\times -1)-1\\-8=a-b-1\\a-b=-7...(i)[/tex]
For the point (1, 2) ,
[tex]y = ax^{2} + bx -1[/tex]
[tex]2=(a\times (1)^{2})+(b\times 1)-1\\2=a+b-1\\a+b=3...(ii)[/tex]
Add the two equations and solve for a as follows:
[tex]a-b=-7\\a+b=3\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\2a = -4\\a = -2[/tex]
Substitute a = -2 in (i) and solve for b as follows:
[tex]a-b=-7\\-2-b=-7\\b=5[/tex]
Thus, the quadratic function is:
[tex]f(x)=-2x^{2}+5x-1[/tex]
The correct option is (b).
(2)
The ordered pairs are:
(5, 7), (7, 11), (9, 14), (11, 18)
Represent them in an XY table as follows:
X : 5 | 7 | 9 | 11
Y : 7 | 11 | 14 | 18
Compute the difference between the Y values as follows:
Diff = 11 - 7 = 4
Diff = 14 - 11 = 3
Diff = 18 - 14 = 4
Now compute the difference between the Diff values:
d = 3 - 4 = -1
d = 4 - 3 = 1
Since the differences between the differences of the y-values is not consistent, the ordered pairs do not represent a quadratic equation.
The correct option is D.
