Answer:
[tex]\displaystyle f(x) = -17(x-1)^2[/tex]
Step-by-step explanation:
We want to write a quadratic function in vertex form whose vertex is (1, 0) and passes through the point (2, -17).
Recall that vertex form is given by:
[tex]\displaystyle f(x) = a(x-h)^2 + k[/tex]
Where (h, k) is the vertex and a is the leading coefficient.
Since our vertex is at (1, 0), h = 1 and k = 0:
[tex]\displaystyle f(x) = a(x-1)^2[/tex]
It passes through the point (2, -17). Hence, when x = 2, y = -17:
[tex]\displaystyle (-17) = a((2)-1)^2[/tex]
Solve for a:
[tex]\displaystyle a = -17[/tex]
In conclusion, our quadratic function in vertex form is:
[tex]\displaystyle f(x) = -17(x-1)^2[/tex]
