So I’m in 10th grade academic math and my teacher is pretty good at explaining concepts, formulas, etc. But the one thing I can’t seem to grasp her explaining of is quadratic equations and parabola, can anyone explain it simply?
In: Mathematics
* A quadratic equation is in the form ax^2 + bx + c = 0
* When you plot it on a graph i.e. y = ax^2 + bx + c, the shape you get is a parabola. It looks like a ∪ or a ∩.
* By changing a,b,c you can stretch it and move it, but it will always look like a ∪ or a ∩, both arms in same direction.
* By looking at the parabola you can infer things about it’s equation. If it looks like ∪ then *a* is positive. If it looks like ∩ then *a* is negative.
* If both arms intersect the x-axis (i.e. y = 0), then it has 2 real solutions. If just the tip touches the x-axis then it has 1 real solution. If it doesn’t touch the x-axis at all it has no real solutions.
* The reason these zeros are important is because they tell you how to factor the equation. Finding the zeros is equivalent to factoring and vice-versa.
* You will spend a lot of time on factoring quadratic equations. E.g. turning x^2 + x – 6 into (x – 2)(x + 3). If you plot that, it will intersect the x-axis at x = 2 and x = -3.
* Sometimes there are no real factors e.g. x^2 + 1 = 0. If you plot that one, it doesn’t touch the x-axis at all.
Latest Answers