Question

How are the coordinates of the extreme value and the equation from part B in the form y=(x-h)^2-c related.

Answer 1

The extreme value of y = (x - h)² - c is the vertex of the equation.

What are extreme values of a function?

The extreme values of a function are either the maximum or minimum values of the function.

The equation of a parabola in vertex form

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,

• h = h'
• -c = k and
• a = 1.

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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