It's easy as 1-2-3
Vertex FormThe 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).
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.