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

Question 1210355: what does the 'a' in the quadratic equation y=ax^2+bx+c represent?

Answer by math_tutor2020(3817) (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

In contrast, now consider y = -4x^2-7x+1 where a = -4 this time.
The parabola opens downward because a < 0.

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

RELATED QUESTIONS
what does the a, b, and c mean in the quadratic equation... (answered by usyim88hk)

What shape is the graph of a quadratic equation in the form... (answered by stanbon)

given a quadratic equation in standard form y=ax^2+bx+c, explain what the coefficient of... (answered by Fombitz)

Q. If one complex zero of a quadratic equation is 2 + i, what is the quadratic equation... (answered by Earlsdon,ichudov)

derive the quadratic formula from... (answered by jim_thompson5910)

what effect does the coefficient a have on the whole equation... (answered by Alan3354)

Write a quadratic equation of the form y=ax^2+bx+c with the given x-intercepts (3,0) and (answered by josmiceli)

what does a mean in the equation ax^2 + bx+c? answer as soon as you... (answered by askme)

a quadratic graph has maximum point (2,5) and passes through point (0,-3). Find the... (answered by Fombitz)