Given the equation 4x2 − 8x + 20 = 0, what are the values of h and k when the equation is written in vertex form a(x − h)2 + k = 0?
h = 4, k = −16
h = 4, k = −1
h = 1, k = −24
h = 1, k = 16

The correct option is:

h = 1, k = 16

Step-by-step explanation:

y=4x^2-8x+20 =0

It is a quadratic formula in standard form:

ax^2+bx+c

where a = 4 , b = -8 and c=20

The vertex form is:

a(x − h)2 + k = 0

h is the axis of symmetry and (h,k) is the vertex.

Calculate h according to the following formula:

h = -b/2a

h= -(-8)/2(4)

h = 8/8

h = 1

Substitute k for y and insert the value of h for x in the standard form:

ax^2+bx+c

k = 4(1)^2+(-8)(1)+20

k = 4-8+20

k=-4+20

k = 16

Thus the correct option is h=1, k=16

The slope of the perpendicular line  m =6

Step-by-step explanation:

Step(i):-

Given that the equation of the straight line

                                            2x + 12y =-192

                                        ⇒ 12 y = -192 -2x      

                                             y = m x +C

The slope of the given line

Step(ii):-

The slope of the perpendicular line

                                   =

The slope of the perpendicular line m =6