Jackie is analyzing a quadratic function f(x) and a linear function g(x). Will they intersect?

Question

anonymous · Answer

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anonymous · Answer

@Michele_Laino

michele_laino · Answer

a quadratic function f(x), can be this:
$$f\left( x \right) = a{x^2} + bx + c$$
whereas a linear function, g(x), can be this:
$$g\left( x \right) = kx + h$$

michele_laino · Answer

now, the intersections between those functions, are given by the solutions of the subsequent algebraic system:
$$\left\{ \begin{gathered}
  f\left( x \right) = a{x^2} + bx + c \hfill \
  g\left( x \right) = kx + h \hfill \ 
\end{gathered}  \right.$$

michele_laino · Answer

so, we can have the subsequent cases:
1) two distinct solutions, which means, taht we have two distinct point of intersections:
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