Question

Find the equation for the parabola that passes through the point (-2,-4), with vertex at (3,1) and a vertical axis

of symmetry.​

Answer 1

see explanation

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, 1), hence

y = a(x - 3)² + 1

To find a substitute (- 2, - 4) into the equation

- 4 = a(- 2 - 3)² + 1

- 4 = 25a + 1 ( subtract 1 from both sides )

25a = - 5 ( divide both sides by 25 )

a = -
`(5)/(25)` = -
`(1)/(5)`

y = -
`(1)/(5)` (x - 3)² + 1 ← in vertex form