SOLUTION: what does the 'a' in the quadratic equation y=ax^2+bx+c represent?

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Question 1210355: what does the 'a' in the quadratic equation y=ax^2+bx+c represent?
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

The 'a' is the leading coefficient.
a, b, and c are placeholders for values.

If a > 0 then the parabola opens upward.
For example consider y = 3x^2+5x-2 where a = 3
graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C-100%2C3x%5E2%2B5x-2%29


In contrast, now consider y = -4x^2-7x+1 where a = -4 this time.
The parabola opens downward because a < 0.
graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C-100%2C-4x%5E2-7x%2B1%29

I recommend using either Desmos or GeoGebra as a graphing tool.
There are many other similar tools as well.

Here is an interactive Desmos graph where you can adjust the value of 'a' to any number you want.
Move the slider around to see how the graph changes.
https://www.desmos.com/calculator/e0boawqc3q