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Diagram 2 shows the graph of a quadratic function f(x) =3+p (x-r)²Finda) value of p,q and rb) if the graph is reflected about to y-axis, write the equation of the curve

Diagram 2 Shows The Graph Of A Quadratic Function Fx 3p XrFinda Value Of Pq And Rb If The Graph Is Reflected About To Yaxis Write The Equation Of The Curve class=

Sagot :

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]

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