Question

Please help me with this problem: I have attach the image to the problem Solve the system of equations by hand using the graphing method. Provide the mathematical steps taken to reach each point for the graphs especially the quadratic equation since those require specific calculations. Graph the functions and state the solution(s).

Answer 1

Given the function

`\begin{gathered} f(x)=-x+5 \\ g(x)=x^2-3x+2 \end{gathered}`

We can find the graph of the function below.

Step-by-step explanation

First, we will pick points for the x -coordinates. The set of suitable values for f(x) will be in the range

`-3\leq x\leq3`

The set of suitable values for g(x) will be in the range

`-3\leqslant x\leqslant5`

Part A: Table of values for f(x) i.e y

`\begin{gathered} When\text{ x =-3} \\ y=-x+5=-(-3)+5=8 \\ when\text{ x=-2} \\ y=-(-2)+5=7 \\ when\text{ x =-1} \\ y=-(-1)+5=6 \\ when\text{ x =0} \\ y=(0)+5=5 \\ when\text{ x =1} \\ y=-1+5=4 \\ when\text{ x=2} \\ y=-2+5=3 \\ when\text{ x= 3} \\ y=-3+5=2 \end{gathered}`

Therefore the table of values for f(x) becomes

Part B: Table of values for g(x) i.e y

`\begin{gathered} when\text{ x=-3} \\ y=x^2-3x+2=(-3)^2-3(-3)+2=20 \\ When\text{ x = -2} \\ y=(-2)^2-3(-2)+2=12 \\ When\text{ x= -1} \\ y=(-1)^2-3(-1)+2=6 \\ when\text{ x =0} \\ y=(-0)^2-3(-0)+2=2 \\ When\text{ x= 1} \\ y=(1)^2-3(1)+2=0 \\ when\text{ x= 2} \\ y=(2)^2-3(2)+2=0 \\ when\text{ x= 3} \\ y=(3)^2-3(3)+2=2 \\ When\text{ x =4} \\ y=(4)^2-3(4)+2=6 \\ when\text{ x=5} \\ y=(5)^2-3(5)+2=12 \\ \end{gathered}`

The table of values

Therefore, we can plot the graph below