Week 11 – solving systems of equations by graphing

This week our class continued even more on quadratic equations (I believe it’s the 3rd chapter that has something to do with quadratics already), and I had learned how to solve 2 types of equations (linear-quadratic and quadratic-quadratic) graphically. At the weekend, I worked on some question and came across one that was particularly interesting. This question asked me to find out the intersections of 2 equations, which they all turned out to all be parabolas: y=-2(x+3)^2-4 and y=-2x^2-12x-22

I decided to turn the second equation to standard form only to find out that it’s y=-2(x+3)^2-4, which was exactly the same as the first equation. To my conclusion (after I looked at the answers for double checking), quadratic-quadratic parabolas on a graph can have 2, 1, 0, or infinite intersections, compared to a linear-quadratic graph (2, 1, 0).

Below is a graph for said question (the yellow broken line and the black dotted line overlay each other):

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