Respuesta :
f(x) has vertex = (- 1, - 5 ) and is a minimum
g(x) has vertex = (2, 3 ) and is a maximum
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
f(x) = (x + 1)² - 5 is in this form with vertex = (- 1, - 5 ) and minimum
to determine if maximum/ minimum
• if a > 0 then minimum
• if a < 0 then maximum
g(x) = - (x - 2)² + 3 is also in vertex form with a < 0
vertex = (2, 3 ) and is a maximum
The vertex of the function f(x) is (-1,-5), the vertex of the function g(x) is (2,3), and the vertex of the function f(x) is minimum and the vertex of the function g(x) is maximum.
Given :
- [tex]\rm f(x)=(x+1)^2-5[/tex]
- [tex]\rm g(x)=-(x-2)^2+3[/tex]
The following steps can be used in order to determine the vertex of each function:
Step 1 - The generalized equation of a parabola in the vertex form is given by:
[tex]\rm y = a(x-h)^2+k[/tex]
Step 2 - So, the vertex of the function f(x) is (-1,-5).
Step 3 - So, the vertex of the function g(x) is (2,3).
Step 4 - Now, if (a > 0) then the vertex of the function is minimum, and if (a < 0) then the vertex of the function is maximum.
Step 5 - The vertex of the function f(x) is minimum and the vertex of the function g(x) is maximum.
For more information, refer to the link given below:
https://brainly.com/question/8823135
