Question

What is the equation in vertex form of a parabola with a vertex of (–3, 4) that passes through the point (1, –4)

Answer 1

The equation in vertex form of the parabola is y = (-1/8)(x + 3)^2 + 4.

Step-by-step explanation:

The equation of a parabola in vertex form is given by y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola. In this case, the vertex is (-3, 4), so the equation becomes y = a(x + 3)^2 + 4.

To find the value of a, we can substitute the coordinates of the given point (1, -4) into the equation. -4 = a(1 + 3)^2 + 4.

Solving this equation, we get a = -2/16 = -1/8. Therefore, the equation of the parabola in vertex form is y = (-1/8)(x + 3)^2 + 4.

Answer 2

y = -
`(1)/(2)` (x + 3)² + 4

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, 4 ) , then

y = a(x - (- 3) )² + 4 , that is

y = a(x + 3)² + 4

to ind a substitute the point (1, - 4 ) into the equation

- 4 = a(1 + 3)² + 4

- 4 = a(4)² + 4 ( subtract 4 from both sides )

- 8 = 16a ( divide both sides by 16 )

-
`(8)/(16)` = a , that is

a = -
`(1)/(2)`

y = -
`(1)/(2)` (x + 3)² + 4 ← equation of parabola