Question

Prove that y=2x^2-6x+7 and y=x^2-2x+3 touch each other and find the point of contact

Answer 1

Answer:

See below ~

Step-by-step explanation:

We need to prove they are equal.

Equate the values to each other.

• 2x² - 6x + 7 = x² - 2x + 3
• x² - 4x + 4 = 0
• (x - 2)² = 0
• x = 2

Now input the x-value in the 1st equation.

• y = 2(2)² - 6(2) + 7
• y = 8 - 12 + 7
• y = -4 + 7
• y = 3

Now input the same in the 2nd equation.

• y = (2)² - 2(2) + 3
• y = 4 - 4 + 3
• y = 3

Since the same x-value, on inputting in both equations, give the same y-value, it is proved they touch each other.

Point of Contact

• (x, y)
• (2, 3)