Standard Form (Quadratic Functions)
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
Standard form of a quadratic equation refers to the general way of writing a quadratic equation as:
y = ax^2 + bx + c
where:
a, b, and c are constants, and a does not equal 0 (because if a = 0, it would no longer be a quadratic equation).
a affects the direction and width of the parabola. If a is positive, the parabola opens upward; if a is negative, it opens downward.
b denotes the slope at which the graph intersects the y-axis
c represents the y-intercept, which is the value of y when x = 0.
Example:
For the quadratic equation y = 2x^2 - 4x + 3, this is in standard form, where:
a = 2
b = -4
c = 3
The standard form is useful for solving quadratic equations, finding the vertex using formulas, and understanding the general shape of the parabola.