if we look at the different graphs shown for quadratic functions we can see that this type of function has symmetry along the vertical line formed at the vertex. Also, the domain usually integrates all the numbers along the x-axis, this means that the domain is all real numbers, however, the range is going to be different, this is going to depend on the concavity, there are two types of concavities for quadratic functions: when the function is concave up the graph is bending upwards, this means that the range will be the numbers greater than the vertex, this is because the graph won't take place at the y-axis for this numbers; when the function is concave down the graph is bending downwards and the range will be opposite as before, the range is going to be the numbers less than the vertex. Finally, another typical thing about this type of function is that the function might be decreasing or increasing depending on the concavity but when it reaches the vertex of the function the direction will change meaning that if it was decreasing, after the vertex it will start increasing, or if the function was increasing, after the vertex it will start decreasing.
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