During this week we did lots of review for the upcoming midterm and during this review I made some connections I didn’t make before that further developed my understanding of the content. One specific thing that stood out to me was a connection I made between when we were factoring/solving quadratics and when we were graphing them. I now understand that when we were finding our roots when solving quadratics, we were really just finding the x intercepts. Also i now see that all of these quadratic equations are essentially just parabolas. For instance, I could have the equation: x^2 + 3x - 4

We normally would have just factored and solved to find the roots, but I made the connection that we could actually use graphs to do this as well.

If you put this into a graph it will look like:

This graph represents x^2 + 3x -4

If we get a closer look we can see the x-intercepts:

The x-intercepts are -4 and 1.

These are actually the solutions to the equation and we can prove this by solving:

x^2 + 3x -4 = 0

 

(x +4) (x -1) = 0

 

x = -4 , x = 1