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Example Question #1 : Pre Calculus
Find the vertex for a parabola with equation
Possible Answers:
Correct answer:
Explanation:
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 #3 : Pre Calculus
What is the minimal value of
over all real numbers?
Possible Answers:
No minimum value.
Correct answer:
Explanation:
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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