Question

The line y = 8x - 4 intersects the parabola y = x^2 + 2x + 5 at exactly one point. What are the coordinates of the point of intersection?

A. (-3, -28)
B. (-3, 8)
C. (3, 3)
D. (3, 20)

Please explain how to solve!!

Answer 1

D.

Explanation:

way №1:

just to substitute the given coordinates into the both equations. Only for answer 'D' will be 20=8*3-4 and 20=3*3+2*3+5.

way №2:

to re-write the right sides as 8x-4=x²+2x+5, then to solve this equation: x²-6x+9=0, where x=3. Then to calculate the value of 'y': y=8*3-4=20. Finally, x=3; y=20, it means (3;20).