FIND POINTS OF INTERSECTION OF PARABOLA AND LINE WORKSHEET

Without using technology, find the coordinates of the point(s) of intersection of:

Problem 1 :

y = x² - 2x + 8 and y = x + 6

Problem 2 :

y = -x² + 3x + 9 and y = 2x - 3

Problem 3 :

y = x² - 4x + 3 and y = 2x - 6

Problem 4 :

y = -x² + 4x - 7 and y = 5x - 4

Problem 5 :

For which value of c is the line y = 3x + c a tangent to the parabola with equation y = x² - 5x + 7 ?

Problem 6 :

Find the values of m for which the lines y = mx - 2 are tangents to the curve with equation y = x² - 4x + 2.

Answer Key

1) Intersection points are (1, 7) and (2, 8).

2) Intersection points are (4, 5) and (-3, -9).

3) intersection point is (3, 0)

4) This expression has no real factors. So, the curves do not intersect.

5) c = -9

6) Hence, m values are 0 and -8.