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Find the vertex and write the quadratic function in vertex form (which our OpenStax textbook also calls the standard form).f(x)=x^2−10 x + 74 Give the vertex. Enter your answer as a point (a,b) .Vertex:Enter the coordinates of the vertex to write f(x) in vertex form:f(x)=(x− )^2+



Answer :

We have the parabola equation in standard form:

[tex]y=ax^2+bx+c[/tex]

and we need to convert it into a vertex form:

[tex]y=A(x-h)^2+k[/tex]

In order to obtain it, we can note that

[tex]f(x)=x^2-10x+74[/tex]

can be rewritten as

[tex]f(x)=(x-5)^2-25+74[/tex]

this is because

[tex](x-5)^2=x^2-10x+25[/tex]

From our last result, we have

[tex]f(x)=(x-5)^2+49[/tex]

By comparing this result with the general vertex form, we can note that

[tex]\begin{gathered} A=1 \\ h=5 \\ k=49 \end{gathered}[/tex]

Therefore, the equation in vertex form is given by:

[tex]f(x)=(x-5)^2+49[/tex]

with vertex:

[tex](h,k)=(5,49)[/tex]

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