What are the vertex, axis of symmetry, maximum or minimum value, domain, and range of the function, and x and y intercepts for f(x)=(x−5)2−9?

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What are the vertex, axis of symmetry, maximum or minimum value, domain, and range of the function, and x and y intercepts for  f(x)=(x−5)2−9?

Rohan Mercado · Accepted Answer

Step 1This is an equation of a parabola, so we can find all the requests easily.y=(x−5)2−9y−yv=a(x−xv)2)The vertex is V(5, −9)The axis of symmetry is a vertical line passing from the vertex, so: x=5The minimum is in the vertex (it is concave up!) and the maximum doesn&#039;t exist (it goes to +∞)The domain is R because it is a polynomial function.The range is [5, +∞)The x intercepts are points whose ordinate are 0, so:0=(x−5)2−9⇒(x−5)2=9⇒x−5=±3⇒x=5±3⇒A(8, 0) and B(2, 0)The y intercept is a point whose ascissa is 0, so:y=(0−5)2−9⇒25−9=16⇒C(0, 16)

What are the vertex, axis of symmetry, maximum or minimum

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