MCR3U Quadratic Functions

[MLS Admin]

Given a quadratic function f(x) and a linear function g(x), describe two ways you could determine the number of points of intersection of the two functions without solving for them.

[Na Yi]

A linear function and a quadratic function can intersect at a maximum of two
points.
• The point(s) of intersection of a line and a parabola can be found
• graphically
• algebraically
To determine the points of intersection algebraically, use substitution
to replace in the quadratic function with the expression for from
the linear function. This results in a quadratic equation whose solutions
correspond to the x-coordinates of the points of intersection.

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