# 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

Solution

Problem 2 :

y = -x2 + 3x + 9 and y = 2x - 3

Solution

Problem 3 :

y = x2 - 4x + 3 and y = 2x - 6

Solution

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 ?

Solution

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.

Solution

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.

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