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

$f\left(x\right)={(x-5)}^{2}-9$ ?

Rohan Mercado

Beginner2022-01-22Added 10 answers

Step 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$V(5,\text{}-9)$

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$+\mathrm{\infty}$ )

The domain is$\mathbb{R}$ because it is a polynomial function.

The range is$[5,\text{}+\mathrm{\infty})$

The x intercepts are points whose ordinate are 0, so:

$0={(x-5)}^{2}-9\Rightarrow {(x-5)}^{2}=9\Rightarrow x-5=\pm 3\Rightarrow$

$x=5\pm 3\Rightarrow A(8,\text{}0)$ and $B(2,\text{}0)$

The y intercept is a point whose ascissa is 0, so:

$y={(0-5)}^{2}-9\Rightarrow 25-9=16\Rightarrow C(0,\text{}16)$

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

The vertex is

The axis of symmetry is a vertical line passing from the vertex, so:

The minimum is in the vertex (it is concave up!) and the maximum doesn't exist (it goes to

The domain is

The range is

The x intercepts are points whose ordinate are 0, so:

The y intercept is a point whose ascissa is 0, so: