Question

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`?

Answer 1

This is an equation of a parabola, so we can find all the requests easily.

`y=(x-5)^2-9`

(`y-y_v=a(x-x_v)^2)`

• The vertex is `V(5,-9)`.
• The axis of symmetry is a vertical line passing from the vertex, so: `x=5`.
• The minimum is in the vertex (it is concave up!) and the maximum doesn't exist (it goes to `+oo`).
• The domain is `RR`, because it is a polynomial function.
• The range is `[5,+oo)`.
• The x intercepts are points whose ordinate are `0`, so:
  `0=(x-5)^2-9rArr(x-5)^2=9rArrx-5=+-3rArr`
  `x=5+-3rArrA(8,0)and B(2,0)`.
• The y intercept is a point whose ascissa is `0`, so:
  `y=(0-5)^2-9rArr25-9=16rArrC(0,16)`.