Given:
[tex]g(x)=2x^2-4x-2[/tex]
Required:
To draw the graph, and then by using the graph we have to fill the blanks.
Explanation:
The graph of the given function is,
Vertex of g(x) is : Vertex" is a synonym for a node of a graph, i.e., one of the points on which the graph is defined and which may be connected by graph edges.
Therefore, from the above graph the vertex is
(1,-4).
The x-intercepts of g are : (-0.414.0,0) and (2.414,0)
The y-intercept is : (0,-2)
Equation of the line of symmetry of g is :
[tex]x=-\frac{b}{2a}[/tex]
Here, a=2
b=-4
Therefore,
[tex]\begin{gathered} x=-\frac{(-4)}{(2)(2)} \\ \\ x=\frac{4}{4} \\ \\ x=1 \end{gathered}[/tex]
g has a (maximum/minimum) of: g has minimum at (1,-4).
Final Answer:
Vertex of g(x) is : (1,-4)
The x-intercepts of g are : (-0.414.0,0) and (2.414,0)
The y-intercept is : (0,-2)
Equation of the line of symmetry of g is : x=1
g has a (maximum/minimum) of: g has minimum at (1,-4).
