Graphs of Linear and Quadratic Functions A linear function is a function that can be expressed in the form of y = mx + b, where: y is the dependen...
Graphs of Linear and Quadratic Functions
A linear function is a function that can be expressed in the form of y = mx + b, where:
y is the dependent variable (the vertical coordinate)
x is the independent variable (the horizontal coordinate)
m is the slope of the line
b is the y-intercept (the point where the line crosses the y-axis)
A quadratic function is a function that can be expressed in the form of y = ax^2 + bx + c, where:
a is the coefficient of the squared term
b is the coefficient of the linear term
c is the constant term
The graph of a linear function is a line with a constant slope. The graph of a quadratic function is a parabola.
Here are some additional points to remember about graphs of linear and quadratic functions:
The slope of a linear function is always positive or zero.
The graph of a quadratic function can have up to two x-intercepts.
The graph of a quadratic function is always symmetric with respect to the line y = x.
Examples:
A linear function with slope 2 and y-intercept (4, 0) would have the equation y = 2x + 4.
A quadratic function with a vertex at (2, 16) and a coefficient a = 1 would have the equation y = x^2 + 16.
By understanding the properties of linear and quadratic functions, we can graph them and analyze their behavior