Question

For the quadratic function f(x)=x^2-6x-27, determine and accurately express each of the key features listed below.

Answer 1

Answer:

1) $(x,y) = (0,-27)$, 2) $V(x,y) = (3, -36)$.

Step-by-step explanation:

1) The ordered pair of the parabola is:

$f(0) = 0^{2} - 6\cdot (0) -27$

$f(0) = -27$

$(x,y) = (0,-27)$

2) The quadratic function needs to be rearranged into the standard form:

$y = x^{2}-6\cdot x -27$

$y = x^{2} - 6\cdot x + 9 -9 -27$

$y = (x-3)^{2}-36$

$y + 36 = (x-3)^{2}$

The vertex is $V(x,y) = (3, -36)$.