## anonymous one year ago Jackie is analyzing a quadratic function f(x) and a linear function g(x). Will they intersect?

1. anonymous
2. anonymous

@Michele_Laino

3. Michele_Laino

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: $g\left( x \right) = kx + h$

4. Michele_Laino

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

5. Michele_Laino

so, we can have the subsequent cases: 1) two distinct solutions, which means, taht we have two distinct point of intersections: |dw:1438611731045:dw|

6. anonymous

Ohhh! :) Ok, I'm understanding it now

7. Michele_Laino

2) one solutions, or more precisely two identical solutions, which means that we have only one intersection: |dw:1438611820605:dw|

8. anonymous

I have to go but I'll be back in 10 minutes(eating breakfast)!

9. Michele_Laino

3) no solutions, which means that we have no intersections: |dw:1438611883205:dw|

10. anonymous

so is it no intersection?

11. anonymous

@Michele_Laino

12. Michele_Laino

yes! in the third case we have no intersections

13. anonymous

yay!:)

14. Michele_Laino

:)