Question

1.) Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth .x squared minus 21 x equals negative 4 x

2.) Which kind of function best models the data in the table? Use differences or ratios.

x y
0 1.7
1 6.8
2 27.2
3 108.8
4 435.2

3.) Solve the system of equations algebraically. Show all of your steps.

y equals x squared plus two x; y equals three x plus twenty



PLEASE HELP!

Answer 1

Answer to number 2 is C) Exponential.

Explanation:

Answer 2

Part 1
We are given
`x^2-21x=-4x`. This can be rewritten as
`x^2-18x=0`.
Therefore, a=1, b=-18, c=0.
Using the quadratic formula

`x=(-b\pm √(b^2-4ac))/(2a)=(-\left(-18\right)\pm √(\left(-18\right)^2-4\left(1\right)\left(0\right)))/(2\left(1\right))`

`x=(18\pm 18)/(2)`

The values of x are

`x_1=(18-18)/(2)=0`

`x_2=(18+18)/(2)=18`

Part 2
Since the values of y change drastically for every equal interval of x, the function cannot be linear. Therefore, the kind of function that best suits the given pairs is a quadratic function.

Part 3.
The first equation is
`y=x^2+2`.
The second equation is
`y=3x+20`.

We have

`x^2+2=3x+20`

`x^2-3x-18=0`
Factoring, we have

`\left(x-6\right)\left(x+3\right)=0`
Equating both factors to zero.

`x_1-6=0\rightarrow x_1=6`

`x_2+3=0\rightarrow x_2=-3`

When the value of x is 6, the value of y is

`y=3\left(6\right)+20=38`

When the value of x is -3, the value of y is

`y=3\left(-3\right)+20=11`

Therefore, the solutions are (6,38) or (-3,11)