Answer :
The equation for the given graph is g(x) = x²-3, and the value of g(2) will be 5.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The equation for the function is,
g(x) = x²-3
The graph of a quadratic function that has something bowl-shaped. Any equation of the form ax²+bx+c=0 where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
To find the value of g (2) the value of the function is,
g(2) = 2²-3
g(2) =8-3
g(2) =5
Thus, the equation for the given graph is g(x) = x²-3, and the value of g(2) will be 5.
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The following information of the quadratic equation is shown below:
(a) g(2) = 1
(b) g(x) = - 2: x = 1 or x = - 1
How to derive information from the graph of a quadratic function
The figure of a quadratic equation set on Cartesian plane is set. from which we must derive information from the domain and range of the function.
In accordance with function theory, the domain of the function, that is, the set of all values x such that function exists, is contained in the horizontal axis and the range of the function, that is, the set of all values y such that function exists, is contained in the vertical axis.
Thus, we proceed to derive the following information from graph:
(a) g(2) = 1
(b) g(x) = - 2: x = 1 or x = - 1
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