High School Math : Parabolas

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #5 : Pre Calculus

Find the vertex  for a parabola with equation

Possible Answers:

Correct answer:


For any parabola of the form   ,  the -coordinate of its vertex is 


So here, we have


We plug this back into the original equation to find :

Example Question #6 : 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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