The equation of a parabola is y=x^2–4x+13. Write the equation in vertex form. Simplify any fractions.

vertex form : y=(x-2)^2+9

Step-by-step explanation:

To convert a parabola from standard form y=x^2-4x+13 to vertex form, we complete the square.

first, complete the square using the x-terms, use the constant term to adjust and make a perfect square.

y=  x^2-4x+4   +  9

Factor the first three terms on the right-hand side.

y=(x-2)^2 + 9

the resulting express is then the vertex form, which means that

the vertex is at (x-2) = 0, x=2, and at y=9.  

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!