For the function y = x2 - 6x + 8, perform the following tasks?

Question

Put the function in the form y = a(x - h)2 + k. and then
What is the equation for the line of symmetry for the graph of this function?
Answer:

Answer 1

Alright.

to put the function into that form, we need to "complete the square". To do so we look to the middle term, -6x. If you take half of the 6, this tells you what number will be going into the parenthesis with the x. In this case, it will be -3. This is our -h. As for the k, what you need to do to find this is to square our h value (3) and figure out the difference between that and the digit we were given at the end of the problem, in this case, 8. 3^2 is 9, the difference between that 8 and our 9 is -1. Since there is no number before the x^2 in this equation, a=1. So our new form looks like this:

y=1(x-3)^2 -1
or
y=(x-3)^2 -1

This form of the equation gives the vertex of the parabola. The vertex is at (3,-1). The vertex gives us the line of symmetry since the line of symmetry goes through the vertex, and its the line x=3.

Answer 2

a) remedy by technique of factorising x2 - 6x + 8 = 0 split the 8 into its factors, and then perceive 2 which upload to provide -6 and multiply to provide 8. you should get -2 and -4. hence, (x-2)(x-4) = 0 --- ab = 0, a=0 or b=0 x= 2 or 4. --------------------------- b) remedy utilising the quadratic formula. x= [-b±?(b2 - 4ac)] / 2a in x2 - 6x + 8 = 0, a = a million, b = -6 and c = 8 x = [6±?(36-32)] / 2 x = [6±2]/2 x = 2 or 4 --------------------------- 2) For the function y = x2 - 6x + 8, carry out right here initiatives: a) placed the function interior the kind y = a(x - h)2 + ok. This contains ending up the sq.. y = x2 - 6x + 8 y = x2 - 6x + 9 - a million y = (x-3)2-a million ---------------------------- b) what's the equation for the line of symmetry for the graph of this function? From area (a), the equation for the line of symmetry is x=h, hence x = 3 ---------------------------- c) [Graph] that's not had to plot factors, as you'll discover the equation of the line of symmetry, the vertex or turning element and intercepts very actual. ---------------------------- d) The graph has an same structure, yet is shifted a million unit down, and three instruments to the right. ---------------------------- 3) you're given the final equation and all the variables, so in basic terms pop them in and also you get: s = -16t2 + 32t --------------------------- b) Sub in t=a million, s = -16(a million)2+32(a million) = 16ft. --------------------------- c) even as it hits the floor, the s = 0. 0 = -16t2 + 32t 0 = t2 - 2t 0 = t(t-2) t = 0 or 2 seconds. Discarding the 0 answer, we get t = 2 seconds. ---------------------------- d) the optimal good is halfway between launch and hitting the floor, at t = a million 2d. you should use the reply from b, 16ft. ----------------------------------- 4) The equation for the fringe is: 2(l+w) = 400ft. l + w = 200ft. l = 2 hundred - w. The equation for the area is A = l x w. sub in (2 hundred-w) for l, A = w(2 hundred-w) A = - w2 + 200w we ought to discover the turning (optimal) element. The equation for the line of symmetry is -b/2a = -2 hundred/-2 = one hundred hence on the max, w = 100ft and l = 2 hundred-one hundred = 100ft. the area right that's 10,000 ft2.

Answer 3

y = x² - 6x + 8
y= (x² - 6x + 9) - 9 + 8
y = (x - 3)² - 1
This is of form y = a(x - h)² + k where a = 1, h = 3 and k = -1
Line of symmetry is x = 3

Answer 4

Do your own homework.
You won't learn anything if I answer it for you.