need help

Question

Write the equation of the parabola with a vertex (-3,5) that opens down and is congruent to the parabola y= 2x^2.

Answer 1

Vertex form of parabola y = a(x - h)² + k

Parabola the y = 2x²

y = 2(x - 0)² + 0

Compare it to y = a(x - h)² + k

(h, k) = (0, 0)  and a = 2

And required parabola  congruent to the y = 2x²

So the vertex shifts from (0, 0) to ( -3, 5)

And it is opens down so a is negative.

Substitute a = -2, (h, k) = (-3, 5) in y = a(x + 3)² + 5

y = - 2(x -(-3))²  + 5

Required parabola equation is y = - 2(x + 3)²  + 5.