Any quadratic function q can be written in the form
q(x)=a(x−h)2+k,where a, h, and k are constants and (h, k) is the vertex of the parabola when q is graphed in the coordinate plane.
(Depending on the sign of a, the constant k must be the minimum ormaximum value of q, and h is the value of x for which a
(x−h)2=0 and q(x) has value k.)
This form can be reached by completing the square in the expression that defines q.
The given equation is
y=x2−2x−15, and since the coefficient of x is −2,the equation can be written in terms of
(x−1)2=x2−2x+1 as follows:
y=x2−2x−15=(x2−2x+1)−16=(x−1)2−16
.
From this form of the equation, the coefficients of the vertex can be read as
(1,−16)Choices A and C are incorrect because the coordinates of the vertex A donot appear as constants in these equations.
Choice B is incorrect because it is not equivalent to the given equation.