Given the graph of the function:
[tex]f(x)=3+p(x-r)^2[/tex]
From the graph of the function:
Vertix = (2, q)
The y-intercept = (0, 23)
We will find the values of p, q, and r
From the point of the vertex of the graph: r = 2, q = 3
And from the point of the y-intercept
When x = 0, f(x) = 23 and substitute with r
so,
[tex]23=3+p(0-2)^2[/tex]
Solve the equation to find p
[tex]\begin{gathered} 23-3=4p \\ 20=4p \\ p=\frac{20}{4}=5 \end{gathered}[/tex]
so, the answer of part A:
[tex]\begin{gathered} p=5 \\ q=3 \\ r=2 \end{gathered}[/tex]
b) if the graph is reflected about to y-axis, write the equation of the curve
So, the equation of the function will be:
[tex]f(x)=-(3+5(x-2))[/tex]
simplifying the equation
So,
[tex]f(x)=-3-5(x-2)[/tex]
