![]() ![]() There are also other ways of describing everything about a parabola, but this is often one of the simplest ways of doing so. To completely describe any parabola, all someone needs to know is: its dilation factor and the coordinates of its vertex. ![]() These three values, a, h, and k, will describe a unique parabola. 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. K determines the y-coordinate of the graph's vertex. For all values of x other than h, the squared quantity in parentheses must produce a value greater than zero (higher than 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. Demonstrate the ability to write a quadratic equation in vertex form. We know that the standard form of the parabola is yax 2 +bx+c. In this article, we are going to learn the standard form and vertex form of a parabola, vertex formula, and examples in detail. H determines the x-coordinate of the graph's vertex. Alternatively, we can just find the vertex as: (-b/2a, f(-b/2a)). If the coefficient of x 2 is negative, then the vertex should be at the top of the U-shaped curve. 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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