# Quadratics

### It's easy as 1-2-3

**Vertex Form**

- (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).

**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.

**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.

**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.