angelamaebrooke
contestada

PLEASE HELP! 30 POINTS!
The functions of f(x) = -(x-1)^2 - 2 and g(x) = (x+2)^2 + 1 have been rewritten using the completing-the-square method. State the vertex for each function. Is the vertex for each function a minimum or maximum? Explain your reasoning for each function.

Respuesta :

nonsibi

These equations are already in vertex form. So, we can easily find the vertex of each equation.

f(x) = -(x-1)^2 - 2

Vertex: (1,-2)

The vertex in this equation is the maximum because it faces down (a=-1).

g(x) = (x+2)^2 + 1

Vertex: (-2,1)

The vertex in this equation is the minimum because it faces up (a=1).

vbreeze1733

The vertex for f(x)=(x+1)^2-2 would represent a minimum because the coefficient of the binomial (x+1) squared term is positive (understood to be in front of the parenthesis). Think about the Vertex From: y=a(x-h)^2+k where "a" is the coefficient of the binomial and(h, k) is the vertex. If "a" is positive the parabola opens up U (Making the vertex the lowest point of the graph). If "a" is negative the parabola opens down N (making the vertex the highest point of the graph)

Therefore:

The vertex of f(x) is a minimum because a=1.

The vertex of g(x) is a maximum because a=-1.