Question

write a quadratic function in vertex form whose graph has the vertex (1,0) and passes through point (2,-17)

Answer 1

Answer:

$\displaystyle f(x) = -17(x-1)^2$

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:

$\displaystyle f(x) = a(x-h)^2 + k$

Where (h, k) is the vertex and a is the leading coefficient.

Since our vertex is at (1, 0), h = 1 and k = 0:

$\displaystyle f(x) = a(x-1)^2$

It passes through the point (2, -17). Hence, when x = 2, y = -17:

$\displaystyle (-17) = a((2)-1)^2$

Solve for a:

$\displaystyle a = -17$

In conclusion, our quadratic function in vertex form is:

$\displaystyle f(x) = -17(x-1)^2$