Question

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

Answer 1

Answer:

${y}^{2} = \frac{4}{3} x$

Step-by-step explanation:

Master equation:

$y {}^{2} = 4 {ax}$

with point ( -3, -2 ):

${( - 2)}^{2} = 4a( - 3) \\ 4 = - 12a \\ a = - \frac{1}{3}$

Equation is:

${y}^{2} = \frac{4}{3} x$

Answer 2

Answer:

y = x² + 6x + 7

Step-by-step 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