**Matched Exercise:** Find the equation of the quadratic function f whose graph has x intercepts at (-1 , 0) and (3 , 0) and a y intercept at (0 , -4).

**Answer to Above Exercise:**

f(x) = (4/3)(x + 1)(x - 3)

**Matched Exercise:** Find values of the parameter c so that the graph of the quadratic function f given by

f(x) = x^{2} + x + c

and the graph of the line whose equation is given by

y = 2x

have:

a) 2 points of intersection,

b) 1 point of intersection,

c) no points of intersection.
**Answer to Above Exercise:**

Find the x coordinates of the point of intersections by solving

x^{2} + x + c = 2x

Rewrite the above equation in standard form

x^{2} - x + c = 0

Find the discriminant D

D = 1 - 4c

If D is positive or c < 1 / 4 , the two graphs intersect at two points.

If D is equal to 0 or c = 1 / 4 , the two graphs intersect (touch) at 1 point.

If D is negative or c > 1 / 4 , the two graphs have no point of intersection.