Question

Find an equation in standard form of the parabola passing through the points. (2,-20),(-2,-4), (0, -8)

Answer 1

The equation of a parabola in standard form is

`y\text{ }=ax^2\text{ + bx + c}`

So, we have the following equations,

For ( 2, -20) , -20 = a(2)^2 + b (2) + c,

For (-2, -4), -4 = a( -2)^2 + b (-2) + c,

For (0.-8), -8 = a (0) + b (0) + c

Then solving,

4a + 2b + c = -20 .............. equ 1

4a - 2b + c = -4 ................... equ 2

c= -8

put c= -8 in equ 1,

we have

4a + 2b -8 = -20 = 4a + 2b = -12 ------equ 3

put c= -8 in equ 2,

4a - 2b -8 = -4 = 4a - 2b = 4................... equ 4

Solving equ 3 and equ 4, a= -1 , b= -4

so a =-1, b= -4, c= -8

Then substituting the values in

`y=ax^2\text{ + bx + c}`

`y=-1(x^2)\text{ + -4(x) + }(-8)`

So, y= -x^2 -4x-8