Solve the equation x^2-16x + 54 = 0 by completing the square. Fill in the values of a and b to complete the solutions.

Step-by-step explanation:

I take it that a and b are defined below.

y = a(x - b)^2 + c

y = (x^2 - 16x ) + 54

y = (x^2 - 16x + (16/2)^2) + 54 - (16/2)^2

y = (x - 16x + (16/2)^2) + 54 - 8^2

y = (x - 16x + 8^2) + 54 - 64

y = (x - 16x + 64)  - 10

y = (x - 8)^2  - 10

This should give you a minimum. Go to Desmos and put in the original equation. It should give a minimum at 8,-10

Since I'm not entirely sure how a and be are defined, I will fill it in the way I have defined it.

a = 1

b = - 8

c = - 10

step-by-step explanation:

what is the figure? attach a picture.

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)