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However, the savvy math student will immediately ask, “Does it work every time? Or was there something `special’ or `unusual’ about these particular quadratic functions?” Does it Always Work? Identify the vertex using the quadratic formula, and verify the answer with the standard method. Let’s double check our -coordinate by using the standard method (plugging into the original function). Solution: The quadratic formula for this function is Use the quadratic formula to identify the entire vertex of the function, and then verify the answer using the standard method. Now, let’s try out this idea and find the vertex of a quadratic from just the quadratic formula. The -coordinate’s denominator is just twice as big as the -coordinate’s! Recall that the discriminant of a quadratic function is and it appears under the radical in the quadratic formula:Īlso, notice that the denominator of the -coordinate and -coordinate of the vertex are very similar. Where is the discriminant of the quadratic function. The vertex of a quadratic function can be written as Less well known is the fact that the -coordinate of the vertex can also be obtained easily from the quadratic formula. Many people notice (or are taught) that the Vertex Formula can be found nestled in the Quadratic Formula. Finding the Vertex in the Quadratic Formula The -value of the vertex,, is often referred to in algebra textbooks as The Vertex Formula. Then separately, we will work on finding the vertex of the function since this point defines the lowest (or highest) point on the graph, as well as the line of symmetry.įor the general quadratic function,, the quadratic formula identifies the roots at: When graphing quadratic functions by hand, we will often use the quadratic formula to obtain the roots (or -intercepts) of the function. What many people don’t know is that you can also easily find the vertex of the function by simply looking at the Quadratic Formula! Graphing Quadratic Functions The Quadratic Formula is primarily used to identify the roots ( -intercepts) of a quadratic function. Finding the Vertex in the Quadratic Formula.