In the equation y = ax^2 + c, what does 'c' represent?

In the equation ( y = ax^2 + c ), the term 'c' represents the y-intercept of the quadratic function. The y-intercept is the value of ( y ) when ( x ) is equal to zero. To find the y-intercept, substitute ( x = 0 ) into the equation:

[

y = a(0)^2 + c = c

]

This means that when the graph of the function intersects the y-axis, it does so at the point ( (0, c) ). Therefore, 'c' indicates where the graph will cross the y-axis, thus confirming that it is indeed the y-intercept.

Understanding this concept is crucial for graphing quadratic functions as it helps establish the initial position of the curve in relation to the axes.