Given:
The table in the data represents the quadratic function.
We need to determine the equation of the function.
The general form of the quadratic equation is [tex]y=ax^2+bx+c[/tex]
Let us substitute the three coordinates (1,5), (2,14) and (3,29) in the general form.
Thus, we have;
[tex]5=a+b+c[/tex] ------ (1)
[tex]14=4a+2b+c[/tex] ------ (2)
[tex]29=9a+3b+c[/tex] ------(3)
Subtracting (2) from (1), we get;
[tex]9=3a+b[/tex] --------- (4)
Subtracting (3) from (2), we get;
[tex]15=5a+b[/tex] -------- (5)
Subtracting (5) from (4), we have;
[tex]6=2a[/tex]
[tex]3=a[/tex]
Thus, the value of a is 3.
Substituting the value of a in equation (4), we get;
[tex]9=3(3)+b[/tex]
[tex]9=9+b[/tex]
[tex]0=b[/tex]
Thus, the value of b is 0.
Substituting a = 3 and b = 0 in equation (1), we get;
[tex]5=3+0+c[/tex]
[tex]5=3+c[/tex]
[tex]2=c[/tex]
Thus, the value of c is 2.
Hence, substituting a = 3, b = 0 and c = 2 in the general form of the quadratic equation [tex]y=ax^2+bx+c[/tex], we get;
[tex]y=3x^2+0x+2[/tex]
[tex]y=3x^2+2[/tex]
Therefore, the function that represents the data in the table is [tex]y=3x^2+2[/tex]
Hence, Option B is the correct answer.
Answer:
B. y = 3x2 + 2
Step-by-step explanation:
just go it correct on edge
