Classes: Quadratic Functions

Specifications

Use the general equation: $$y = a x^2 + b x + c \tag{1}$$ Required methods:

1. Return the value of y for a given x (f(x)).
2. Return the x coordinate of the vertex.
3. Return the y coordinate of the vertex.
4. Return both the x and y coordinates of the vertex.
5. Return the y-intercept
6. Find the zeros of the function (the x-intercepts: values of x where y = 0)
7. Print out the equation like: y = x² + 2x - 8
8. Draw the curve.
9. Find the slope of the line at a given x value.

Test

Test your class using the equation: $$y = x^2 + 2x - 8$$

For the equation: y = x² + 2x - 8
(1) If x = 3 then y = 7
(2) The x-coordinate of the vertex is -1.0
(3) The y-coordinate of the vertex is -9.0
(4) The (x, y) coordinates of the vertex are (-1.0, -9.0)
(5) The y-intercept is at y = -8
(6) The x intercepts (zeros) of the function are: [2.0, -4.0]
(7) The human readable form of the equation is: y = x² + 2x - 8
(8) Drawing graph (see below) ...
(9) The slope of the line at x = -1.0: dy/dx = 0.0
(9) The slope of the line at x = 3: dy/dx = 8

Area (by Integration)