Answer:
[tex]y=2(x-4)^2-1[/tex]
Step-by-step explanation:
The vertex form of a parabola is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Vertex form of a quadratic equation}}\\\\y=a(x-h)^2+k\\\\\textsf{where:}\\\phantom{ww}\bullet\;(h,k)\;\sf is\;the\;vertex.\\\phantom{ww}\bullet\;a\;\sf is\;the\;leading\;coefficient.\\\end{array}}[/tex]
To write an equation of a parabola with a vertex at (4, -1) in vertex form, substitute h = 4 and k = -1 into the formula:
[tex]y=a(x-4)^2-1[/tex]
We can choose any value of a. Let's use a = 2:
[tex]y=2(x-4)^2-1[/tex]
Therefore, an equation of a parabola with a vertex at (4, -1) in vertex form is:
[tex]\Large\boxed{\boxed{y=2(x-4)^2-1}}[/tex]
