You could just substitute the values given to see if the equation = 0
try x = -2 does it = 0 if yes , then that is one root if no, then try +2
try 1 and then try -1
4 ( x^2-7x ) - 17
4 ( x-3.5)^2 - 17 - 12.25
4(x-3.5)^2 - 29.25 vertex = 3.5 , - 29,5
y = mx+ b b = y - intercept (this occurs when x=0)
y = -2/3 x -7
Where they intersect , they are equal, sooooo
-3x^2+12x-6 = 2x^2-4x+3 solve for 'x' (there may be more than one) then use this value in one of the equations to find 'y'
there may be 1 2 or zero points of intersection !
Minimum value of x will be -b/2a = - -12/8 = 1 1/2
sub in x = 1.5
4 (1.5)^2 -12 (1.5) + k = - 1
9 - 18 + k = -1
k = 8
apples to pears = 7:4
35/x = 7/4
x = 20 pears
Ooops....I didn't see the volunteers joined after 6 days recalculating!
After adding 28 painters they now have 35 painters to do what would take 7 painters 50 days to complete
7/ 35 x 50 = 10 days to complete
10 x + y = 45 + 10y + x and x+y = 11 or y = 11-x sub this into the first equation
10x + 11-x = 45 + 10(11-x) + x and solve for 'x'
9x + 11 = 45 +110-9x
18x = 144
x = 8 then y = 3 favorite number is 83 reversed = 38 which is 45 less than 83
Put it into standard form of (x-h)^2 + (y-k)^2 = r^2
complete the square for x and y
(x-5)^2 + (y+4)^2 = 18 +25 + 16
(x-5)^2 + (y+4)^2 = 59 soooooo: 59 = r^2 find 'r'
800 - 30x = 300 + 20x solve for 'x' = number of weeks
500 = 50x
x = 10 weeks
