Using the quadratic equation x2 - 6x + 8 = 0, perform the following tasks:?

Answer 1

The Quadratic Equation is: x = [- b +/- V`(b^2 - 4ac)] / 2a

First: you need three values (coefficients) for three variables...
a = 1 > b = - 6 and > c = 8

Sec: place the values in the equation & solve...

x = [- (-6) +/- V`((-6)^2 - 4(1)(8))] / 2(1)

x = [6 +/- V`((-6)^2 - 4(1)(8))] / 2(1)

x = [6 +/- V`((-6)^2 - 4(1)(8))] / 2

x = [6 +/- V`((-6)(-6) - 4(1)(8))] / 2

x = [6 +/- V`(36 - 4(1)(8))] / 2

x = [6 +/- V`(36 - 4(8))] / 2

x = [6 +/- V`(36 - 32)] / 2

x = [6 +/- V`(4)] / 2

x = [6 +/- 2] / 2

Third: you have two solutions, one has addition-the other has subtraction...

a. x = [6 + 2] / 2
x = 8/2
x = 4

b. x = [6 - 2] / 2
x = 4/2
x = 2

Solutions: 2 and 4

Answer 2

a) sparkling up by utilising factorising x2 - 6x + 8 = 0 smash up the 8 into its factors, and then perceive 2 which upload to furnish -6 and multiply to furnish 8. you may get -2 and -4. for this reason, (x-2)(x-4) = 0 --- ab = 0, a=0 or b=0 x= 2 or 4. --------------------------- b) sparkling up 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 includes winding 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, for this reason x = 3 ---------------------------- c) [Graph] that is no longer mandatory to devise factors, as you will detect the equation of the line of symmetry, the vertex or turning factor and intercepts very rather. ---------------------------- d) The graph has an identical shape, yet is shifted a million unit down, and 3 gadgets to the superb. ---------------------------- 3) you're given the final equation and all of the variables, so purely pop them in and you get: s = -16t2 + 32t --------------------------- b) Sub in t=a million, s = -sixteen(a million)2+32(a million) = 16ft. --------------------------- c) while 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 utmost top is midway between launch and hitting the floor, at t = a million 2d. you should use the respond 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 section is A = l x w. sub in (2 hundred-w) for l, A = w(2 hundred-w) A = - w2 + 200w we could continually discover the turning (maximum) factor. The equation for the line of symmetry is -b/2a = -2 hundred/-2 = one hundred for this reason on the max, w = 100ft and l = 2 hundred-one hundred = 100ft. the section right it incredibly is 10,000 ft2.

Answer 3

x=4 x=2

Answer 4

I suppose that by x2 you mean x^2

x =[6 +- sqareroot(6^2 - 4* 8)] /2 = (6 +-2) / 2 =

a) 8/2 = 4

b) 4/2 = 2

So x_1=2, x_2=4

Answer 5

Factorizing:

(x-4)(x-2) so x = 4 and 2

Cuadratic equation:

(-b +-sqrt(sqr(b)-4ac))/2a

(6+-sqrt(36-32))/2 = (6+-2)/2 = 4 and 2

Answer 6

(x-4)(-2)=0

x=4,2, normal factor works

6+-sqrt(36-48)/2(1), can't be done with quadratic formula

b^2