Question

Write the equation of the parabola in vertex form.
vertex (3,4), point (1,-4)

Answer 1

y = - 2(x - 3)² + 4

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

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

- 4 = a(1 - 3)² + 4 ( subtract 4 from both sides )

- 8 = a(- 2)² = 4a ( divide both sides by 4 )

- 2 = a

y = - 2(x - 3)² + 4 ← equation in vertex form