To find the amplitude of a quadratic equation, you need to know its general form, which is given by:
y = ax^2 + bx + c
where:
- y is the dependent variable (output or function value)
- x is the independent variable (input or variable)
- a, b, and c are constants with a ≠ 0. a is the coefficient of the quadratic term, b is the coefficient of the linear term, and c is the constant term.
The amplitude of the quadratic equation is not a standard term for quadratics as it is for periodic functions like sine or cosine waves. However, if you mean the "a" coefficient (coefficient of the quadratic term) as the amplitude, here's how you can find it:
- Given the roots: If you know the roots of the quadratic equation, say x1 and x2, you can express the equation in factored form:
y = a(x - x1)(x - x2)
- Given the y-intercept (c coefficient): The y-intercept represents the value of y when x is zero. So, if you know the y-intercept (c), you can substitute x = 0 into the equation and solve for "c":
y = a(0 - x1)(0 - x2) = a * x1 * x2 = c
Now that you have both expressions for "y," you can equate them:
a(x - x1)(x - x2) = c
- Solve for "a": To find the value of "a," divide both sides of the equation by (x - x1)(x - x2):
a = c / ((x - x1)(x - x2))
With this equation, you can calculate the value of "a" using the known values of c, x1, and x2 (the roots and y-intercept) for the specific quadratic equation you are dealing with.
Please note that the term "amplitude" is more commonly used in the context of periodic functions like sine or cosine waves and doesn't have a direct analog for quadratic functions. The "a" coefficient is related to the width and direction of the parabola, but it doesn't directly correspond to what we typically refer to as amplitude in trigonometry.