Respuesta :
The vertex of a parabolla can be found by using the following expression:
[tex]x=\frac{-b}{2a}[/tex]For this parabolla we have:
[tex]x=\frac{-(-10)}{2\cdot1}=\frac{10}{2}=5[/tex]To find the y-coordinate we can apply the value of x for the vertex and evaluate the expression:
[tex]F(x)=(5)^2-10\cdot5+19=-6[/tex]The vertex is on the coordinates (5,-6).
The vertex form of a parabola is given by:
[tex]f(x)=d\cdot(x-h)^2+k[/tex]Where (h,k) are the coordinates of the vertex for the parabolla. For this parabolla we have:
[tex]f(x)=d\cdot(x-5)^2-6[/tex]To find the value of d we can use the standard expression for the parabolla, as shown below:
[tex]\begin{gathered} f(x)=d\cdot(x^2-10x+25)-6 \\ f(x)=d\cdot x^2-10\cdot d\cdot x+25\cdot d-6 \end{gathered}[/tex]The value of d must make the expression above equal to the original parabolla. Therefore d must be 1.
[tex]f(x)=(x-5)^2-6[/tex]