There are also other ways of describing everything about a parabola, but this is often one of the simplest ways of doing so. Write the equation of the quadratic function shown in vertex form. To completely describe any parabola, all someone needs to know is: its dilation factor and the coordinates of its vertex. A parabola is the graph of a quadratic equation, which is an equation that has its variable, usually x, raised to. These three values, a, h, and k, will describe a unique parabola. How to Convert Standard Form to Vertex Form. This forces the y-coordinate of the vertex to become k. When (at the vertex), the entire squared term will always equal zero, and the result of the equation must equal k. Because the vertex appears in the standard form of the quadratic function, this form is also known as the vertex form of a quadratic function. In other words, for the vertex, (x, y) (h, k). The standard form of a quadratic function presents the function in the form f (x) a(xh)2 +k f ( x) a ( x h) 2 + k where (h, k) ( h, k) is the vertex. K determines the y-coordinate of the graph's vertex. To write the equations of a quadratic function when given the graph: 1) Find the vertex (h,k) and one point (x,y). When graphing a quadratic function with vertex form, the vertexs x and y values are h and k respectively. With this form of the quadratic formula one. For all values of x other than h, the squared quantity in parentheses must produce a value greater than zero (higher than the vertex). The Vertex Form of the quadratic model is :, where a is a constant and (h, k) is the coordinate of the vertex. Therefore, when a is positive, h becomes the x-coordinate at which the graph must reach its lowest point: its vertex. Note that in the equation shown on the graph, when x is equal to h, the value in parentheses must equal zero, which is the smallest value that any squared real quantity can assume. H determines the x-coordinate of the graph's vertex. Note what happens to the graph when you set a to a negative value. It determines how much the graph is stretched away from, or compressed towards, the x-axis. the vertex of the graph (the blue point labelled V) is moved on top of the other blue point on the graph: (-3, -1)Ī is referred to as the "dilation factor". any part of the graph passes through the other blue point on the graph (-3, -1) the graph becomes a horizontal line, or opens down the vertex lies above, or below, the x-axis the vertex lies to the right, or left, of the y-axis Once you understand the effect that each slider has, see if you can adjust the sliders so that:
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