Answer:
Equation of parabola is : [tex]f(x) = 4x^2 + 3x -6[/tex]
Step-by-step explanation:
Given,
x = -2 0 4
f(x) = 4 -6 70
General equation of parabola is:[tex]y = ax^2 + bx + c[/tex]
Now we plug corresponding x and y values to get coefficient a,b and c.
Fro x =-2 and y( =f(x) ) = 4
[tex]4 = a(-2)^2 + b(-2) + c\\4 = 4a -2b + c[/tex] ______(1)
For x = 0 , y = -6
[tex]-6 = a(0)^2 + b(0) + c\\-6 = c[/tex] _____(2)
For x = 4 , y = 70
[tex]70 = a(4)^2 + b(4) + c\\70 = 16a + 4b + c[/tex] _____(3)
Plug c= - 6 in equation (1) and (3)
We get, [tex]4 = 4a - 2b - 6 \\And\\70 = 16a + 4b - 6[/tex]
solving above two equations to find a and b.
Multiply equation (1) by 2 then add equation (1) and (3)
[tex]8 + 70 = 8a + 16a -4b + 4b -12 -6\\78 = 24a - 18\\78 + 18 = 24a\\a = 96/24 = 4\\And b = 3[/tex]
Hence equation of parabola is : [tex]f(x) = 4x^2 + 3x -6[/tex]
