write the equation of the parabola in vertex form. vertex (4,2) , point (2,-6)

Question

write the equation of the parabola in vertex form. vertex (4,2) , point (2,-6)

Answer 1

Vertex form is y= a(x-h)^2 +k where h and k are the x and y coordinates of the vertex And a is scale factor

so y=a(x-4)^2+2

To solve for a use the given point (2,-6)

-6 =a(2-4)^2 +2

-8 =a(-2)^2

-8= a(4)

a=-2

So final equation is y=-2(x-4)^2 +2

You can verify by graphing the equation and you will see its vertex is at(4,2) and it passes thru the point (2,-6)

Answer 2

vertex = (h,k) = (4,2)

point = (x,y) = (2,-6)

vertex form:

y = a(x - h)² + k

Plug in h = 4 and k = 2 from the vertex into the equation. Then plug in x = 2 and y = -6 from the point to solve for a:

y = a(x - h)² + k

y = a(x - 4)² + 2

-6 = a(2 - 4)² + 2

-8 = a(-2)²

-8 = 4a

a = -8 / 4 = -2

y = -2(x - 4)² + 2