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The answers to the exercises in Tutorial on Quadratic Functions are presented here.
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) = x2 + 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
x2 + x + c = 2x
Rewrite the above equation in standard form
x2 - 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.
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