Question

Find the order pairs by following the tablegiven:y=x^2 -12x+36table of x : ?,5,9,4y : 0,?,1,?,?

Answer 1

x = ? , 5 , 9 , 4

y= 0, ? , 1 , ?

To find the missing x value, replace the matching value of y (0) in the equation and solve for x:

0 = x^2-12x +36

Apply the quadratic formula

`\frac{-b\pm\sqrt[]{b^2-4\cdot A\cdot c}}{2\cdot a}=\frac{12\pm\sqrt[]{(-12)^2-4\cdot1\cdot36}}{2\cdot1}`
`\frac{12\pm\sqrt[]{144-144}}{2}=(12)/(2)=6`

For x = 5:

y= (5)^2-12 (5) +36 = 25-60+36 = 1

For y=1

1 =x^2-12x+36

0 = x^2-12x+36-1

0= x^2-12x+35

`\frac{12\pm\sqrt[]{(12)^2-4\cdot1\cdot35}}{2\cdot1}=\frac{12\pm\sqrt[]{144-140}}{2}=(12\pm2)/(2)=(14)/(2)=7\text{ }`

x =7

For x=9

y= (9)^2-12 (9)+36 = 81-108+36=9

For x=4

y= (4)^2-12(4)+35 = 16-48+36=4