What are the similarities and differences between the standard form and vertex form of a quadratic equation?

Question

Mathematics

Gustavo Andrade

23 April, 00:00

What are the similarities and differences between the standard form and vertex form of a quadratic equation?

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Camryn · Answer 1

Answer and Step-by-step explanation: Standard form of a quadratic equation is expressed as: y=ax²+bx+c, while vertex form is written as:

y=a (x-h) ²+k.

The similarities between standard and vertex forms is that they show if the graph of the equation has a minimum (when a>0) or maximum (a<0) and it's easier to determine the y-intercept: for standard, the value of c is the intercept; for vertex, the value k is the intercept.

The advantage of standard form is that you can determine the product and sum of the equation's roots, which is a method to determine them.

The advantages of vertex form are: easier to find the vertex of the graph, which is the pair (h, k) and the axis of symmetry, which is the value of h.