Answer:
y = - 7(x - 4)² + 2
Explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
(h, k ) are the coordinates of the vertex and a is a multiplier
given vertex = (4, 2 ) = (h, k ) , then
y = a(x - 4)² + 2
to find a , substitute the point (3, - 5) , that is x = 3, y = - 5 , into the equation
- 5 = a(3 - 4)² + 2 ( subtract 2 from both sides )
- 7 = a(- 1)² = a
y = - 7(x - 4)² + 2 ← equation of parabola