Tessa Leach

2022-01-21

What are the vertex, axis of symmetry, maximum or minimum value, domain, and range of the function, and x and y intercepts for
$f\left(x\right)={\left(x-5\right)}^{2}-9$?

Step 1
This is an equation of a parabola, so we can find all the requests easily.
$y={\left(x-5\right)}^{2}-9$
$y-{y}_{v}=a{\left(x-{x}_{v}\right)}^{2}\right)$
The vertex is
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 $+\mathrm{\infty }$)
The domain is $\mathbb{R}$ because it is a polynomial function.
The range is
The x intercepts are points whose ordinate are 0, so:
$0={\left(x-5\right)}^{2}-9⇒{\left(x-5\right)}^{2}=9⇒x-5=±3⇒$
and
The y intercept is a point whose ascissa is 0, so:

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