Answer :

Answer:

The correct option is C.

Step-by-step explanation:

The given function is

From the given graph it is clear that the vertex of f(x) and g(x) are same, i.e.,(0,0). But the graph of g(x) compressed vertically.

If k>1, then graph of g(x) stretched vertically and if k<1, then graph of g(x) compressed vertically.  

The graph of g(x) passing through the point (2,2).

The value of k is 1/2. The function g(x) is

Therefore, option C is correct.

ashishdwivedilVT

The correct option is B.; i.e. g(x) = 1/2 x².

What is Quadratic Equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

We want to get g(x) given that we know f(x) and the graphs for both functions.:

g(x) = 1/2 x²

By looking at the graph we can see that f(x) and g(x) are two quadratic functions, and g(x) is just a dilation of f(x).

This means that:

g(x) = A X f(x)

Where A is a real number.

We know that:

f(x) = x²

And by looking at the graph, we also know that g(2) = 2.

Then we can write:

g(2) = A X f(2) = A X 2² = 2

Now we can solve this for A:

A X 2² = 2

A X 4 = 2

A = 2/4

A = 1/2

Then we have:

g(x) = (1/2)f(x) = (1/2) X x² = x²/2

Thus, The correct option is B.; i.e. g(x) = 1/2 x².

Learn more about quadratic equations from:

brainly.com/question/1214333

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