Parabola in vertex form with vertex of (2,1), and point (4,-3)

y = - (x - 2)² + 1

Step-by-step 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) = (2, 1), thus

y = a(x - 2)² + 1

To find a substitute (4, - 3) into the equation

- 3 = a(4 - 2)² + 1, that is

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

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

a = - 1, thus

y = - (x - 2)² + 1 ← in vertex form

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3

17.08

correct me if i am wrong.