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

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
     $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-\left(-18\right)\pm \sqrt{\left(-18\right)^2-4\left(1\right)\left(0\right)}}{2\left(1\right)}$
     $x=\frac{18\pm 18}{2}$

The values of x are
     $x_1=\frac{18-18}{2}=0$
     $x_2=\frac{18+18}{2}=18$

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)