Vertex Form
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
Vertex form of a quadratic equation is a way of expressing the equation that highlights its vertex — the highest or lowest point on its graph (depending on whether the parabola opens up or down). The vertex form is written as:
y = a(x - h)^2 + k
where:
a is a constant that affects the width and direction of the parabola. If a is positive, the parabola opens upwards; if a is negative, it opens downwards.
(h, k) is the vertex of the parabola, meaning it's the point where the parabola reaches its maximum or minimum value.
The vertex form is especially useful for graphing quadratics, as it allows you to quickly identify the vertex and the direction of the parabola.
Example:
For the quadratic equation y = 2(x - 3)^2 + 4, the vertex form shows that:
The vertex is at (3, 4).
The parabola opens upwards because a = 2 is positive.
This form makes it easier to plot the graph and understand the quadratic's key features.