Question

The vertex of parabola is -3,-2, what is the equation?

Answer 1

y = x² + 6x + 7

Explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (- 3, - 2 ) and with a = 1 , then

y = (x - (- 3) )² - 2

= (x + 3)² - 2 ← expand using FOIL

= x² + 6x + 9 - 2

y = x² + 6x + 7 ← equation of parabola

Answer 2

`{y}^(2) = (4)/(3) x`

Explanation:

Master equation:

`y {}^(2) = 4 {ax}`

with point ( -3, -2 ):

`{( - 2)}^(2) = 4a( - 3) \\ 4 = - 12a \\ a = - (1)/(3)`

Equation is:

`{y}^(2) = (4)/(3) x`