The extreme value of y = (x - h)² - c is the vertex of the equation.
<h3>What are extreme values of a function?</h3>
The extreme values of a function are either the maximum or minimum values of the function.
<h3>The equation of a parabola in vertex form</h3>
The equation of a parabola in vertex form with vertex (h', k) is given by
y = a(x - h')² + k and its extreme values are
- if a > 0 (h', k) is a minimum point and
- if a < 0 (h', k) is a maximum point.
Since y = (x - h)² - c is the equation of a parabola in vertex form, comparing with y = a(x - h')² + k,
So, the cooordinates of the vertex of y = (x - h)² - c is (h, -c).
Now, since a = 1 > 0, (h, -c) is a minimum point.
So, the extreme value of y = (x - h)² - c is the vertex of the equation.
Learn more about extreme value of a function here:
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