Quadratics

It's easy as 1-2-3

Vertex Form

The vertex form of a parabola's equation is generally expressed as: y = a(x-h)2+k
  • (h,k) is the vertex as you can see in the picture below
  • The value of k is the vertical (y) location of the vertex and h the horizontal (x-axis) value, they determine the location of the curve but not its shape.
  • If "a" is positive then the parabola opens upwards like a regular "U".
  • If "a" is negative, then the graph opens downwards like an upside down "U".
  • If "a" < 1, the graph of the parabola widens. This just means that the "U" shape of parabola stretches out sideways.
  • If |a| > 1, the graph of the graph becomes narrower (The effect is the opposite of |a| < 1).
Changing a Quadratic Function into Vertex Form

Factored form, the product of a constant and two linear terms. The parameters and are the roots of the function (the x-intercepts of the graph). Converting a quadratic function to factored form is called factoring.

Quadratic Relations of the Form y = a(x r)(x s)

Standard form, the sum of a constant term, and a constant, times the square of a linear term.The vertex of the graph is located at the point . Converting a quadratic function to standard form is called completing the square. In each case the parameter determines the vertical stretching of the graph.

Quadratic Equations in Standard Form

Expanded form, a sum of terms, each of which may be a product of a constant and some variables. The parameter is the y-intercept, while the parameter is the slope of the tangent at 0. Converting a quadratic function to expanded form is called expanding.