We We SOLUTION
Given the question in the image tab, the following are the solution steps to get the quadratic functions
Step 1: Write the zeroes and the y-intercept
[tex]\begin{gathered} \text{roots}=\text{zeroes}=-1\text{ and 5} \\ (x,y)=(0,3),\text{ y-intercept=3} \end{gathered}[/tex]
Step 2: Write the general factored form formula
[tex]f(x)=a(x-r_1)(x-r_2)[/tex]
Step 3: Get the value of a using the zeroes and the points written in step 1
[tex]\begin{gathered} f(x)=a(x-(-1))(x-5) \\ f(x)=a(x+1)(x-5) \\ \operatorname{Re}call\text{ that x=0 and y=3} \\ 3=a(0+1)(0-5) \\ 3=a(1)(-5) \\ 3=-5a \\ a=-\frac{3}{5} \end{gathered}[/tex]
Step 4: Write the quadratic function for the system using the formula in step 2
[tex]f(x)=-\frac{3}{5}(x+1)(x-5)[/tex]
Hence, the quadratic function with the given zeroes and y-intercept in a reduced fraction form will be:
[tex]f(x)=-\frac{3}{5}(x+1)(x-5)[/tex]
