Question

Write an equation of a parabola in standard form that has a vertex of (-3,-4) and passes through (1,4)

Answer 1

As we know vertex -

`y=a(x+3)^2-4`

Passes through (1,4). Substitute x = 1 and y = 4

`4=a(1+3)^2-4\\4=a(4)^2-4\\4=16a-4\\4+4=16a\\16a=8\\a=(8)/(16)\\a=(1)/(2)`

Therefore the vertex equation is
`y=(1)/(2)(x+3)^2-4`

Since you want the "standard" form then..

`y=(1)/(2)(x^2+6x+1)\\y=(1)/(2)x^2+3x+(1)/(2)`

So the standard form is 1/2x^2 + 3x + 1/2