The vertex form of a quadratic function:
(h,k) - the coordinates of the vertex
If a>0, then the parabola opens upwards, so the vertex is the minimum of the
function.
If a<0, then the parabola opens downwards, so the vertex is the maximum of
the function.
F(x) = (x+4)^2+2
A = -1 <0
Vertex is a maximum
G(x) = (x-2)^2-2
A = 1>0
Vertex is a minimum
Answer:
vertex of f(x) is the maximum point.
vertex of g(x) is the minimum point.
Step-by-step explanation:
The given functions are
[tex]f(x)=-(x+4)^2+2\\\\g(x)=(x-2)^2-2[/tex]
These represents parabola. The vertex form of a parabola is given by
[tex]y=a(x-h)^2+k[/tex]
Here, (h,k) is the vertex of the parabola.
Now, the parameter 'a' decides the shape of the parabola.
For the function f(x), a =- 1 and vertex is (-4,2). Since a < 0 hence, parabola opens downward and vertex will be the maximum point.
For the function g(x), a= 1 and vertex is (2,-2). Since a > 0 hence, parabola opens upward and vertex will be the minimum point.
