High School Math : Graphing Parabolic Functions

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #3 : Pre Calculus

What is the minimal value of 

over all real numbers?

Possible Answers:

No minimum value.

Correct answer:


Since this is an upwards-opening parabola, its minimum value will occur at the vertex.  The -coordinate for the vertex of any parabola of the form

is at


So here, 


We plug this value back into the equation of the parabola, to find the value of the function at this

Thus the minimal value of the expression is

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