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:

Find the volume V of the described solid S

A cap of a sphere with radius r and height h.

V=??

Whether each of these functions is a bijection from R to R.

a) $f(x)=-3x+4$

b) $f\left(x\right)=-3{x}^{2}+7$

c) $f(x)=\frac{x+1}{x+2}$

?

$d)f\left(x\right)={x}^{5}+1$In how many different orders can five runners finish a race if no ties are allowed???

State which of the following are linear functions?

a.$f(x)=3$

b.$g(x)=5-2x$

c.$h\left(x\right)=\frac{2}{x}+3$

d.$t(x)=5(x-2)$ Three ounces of cinnamon costs $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound?

A square is also a

A)Rhombus;

B)Parallelogram;

C)Kite;

D)none of theseWhat is the order of the numbers from least to greatest.

$A=1.5\times {10}^{3}$,

$B=1.4\times {10}^{-1}$,

$C=2\times {10}^{3}$,

$D=1.4\times {10}^{-2}$Write the numerical value of $1.75\times {10}^{-3}$

Solve for y. 2y - 3 = 9

A)5;

B)4;

C)6;

D)3How to graph $y=\frac{1}{2}x-1$?

How to graph $y=2x+1$ using a table?

simplify $\sqrt{257}$

How to find the vertex of the parabola by completing the square ${x}^{2}-6x+8=y$?

There are 60 minutes in an hour. How many minutes are there in a day (24 hours)?

Write 18 thousand in scientific notation.