Graphing Quadratic Functions Using Vertex Form and Intercept Form

Concept

Quadratic Function

A quadratic function is a polynomial function of degree 2 that can always be written in the form y=ax^2+bx+c, with a≠ 0. Notice that the highest exponent of the independent variable is 2. The graph of any quadratic function is a vertical parabola.

parabola

There are three ways to write a quadratic function.

Name Equation Characteristics
Standard Form y=ax^2+bx+c a, b, and c are real numbers, a≠ 0, and c is the y-intercept of the parabola.
Vertex Form y=a(x-h)^2+k a, h, and k are real numbers, a≠ 0, and (h,k) is the vertex of the parabola.
Intercept Form
(also called Factored Form)
y=a(x-x_1)(x-x_2) a, x_1, and x_2 are real numbers, a≠ 0, and x_1 and x_2 are the x-intercepts of the parabola.
Exercises
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