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

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

• A. The leading coefficient
• B. The y-intercept
• C. The point of symmetry
• D. The variable coefficient

Answer: (B)

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.

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.