Question 561145
this is a quadratic equation.
the standard form of a quadratic equation is:
y = ax^2 + bx + c
when a is positive, the quadratic equation goes more positive on each end and has a minimum point in the middle.
when a is negative, the quadratic equation does more negative on each end and has a maximum point in the middle.
i'll make your equation even simpler for demonstration purposes.
assume your equation is y = -2x^2 + 5x - 3
the a term is equal to -2.
that's the coefficient of the x^2 term.
being negative, your quadratic equation will go more negative on both ends and will hit a maximum point in the middle.
the graph of your equation is shown below:
{{{graph(600,600,-5,5,-10,10,-2x^2+5x-3)}}}
if the coefficient of the x^2 term is positive, then the graph goes more positive at the ends and has a minimum point in the middle.
take your same equation and make the a term positive to get:
y = 2x^2 + 5x - 3
the graph of this equation is shown below:
{{{graph(600,600,-5,5,-10,10,2x^2+5x-3)}}}
that is the significance of the a term in your equation.
it's sign determines which way the quadratic equation is pointing.