Answer:
vertex = (- 2, 16 )
Step-by-step explanation:
Given a quadratic in standard form : f(x) = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = - x² - 4x + 12 ← is in standard form
with a = - 1, b = - 4, thus
[tex]x_{vertex[/tex] = - [tex]\frac{-4}{-2}[/tex] = - 2
To find the y- coordinate substitute x = - 2 into f(x)
f(- 2) = - (- 2)² - 4(- 2) + 12 = - 4 + 8 + 12 = 16
Vertex = (- 2, 16 )
The vertex of equation -x² - 4x + 12 is (-2, 16).
A vertex or node is the fundamental unit of which graphs are formed: an undirected graph consists ofa set of vertices and a set of edges, whilea directed graph consists of a set of vertices and set of arcs.
Now the given equation is f(x) = -x² - 4x + 12
which is of the form f(x) = ax² + bx + c
where a = -1, b= -4 and c = 12
Let (h,k) be the required vertex of f(x),
and since the the vertex is given as
x = h= -b/2a
Therefore vertex of f(x) is
h = -(-4)/2(-1)
h= - 4/2
h= -2
Since, k = y = f(x)
Putting the value of x in f(x) we get,
f(-2) = -(-2)² -4(-2) + 12
f(-2) = -4 + 8+ 12
f(-2) = 16
Therefore, k = 16
Hence the required vertex(h,k) is (-2, 16).
To learn more about the vertex form :
brainly.com/question/15673828
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