Question

Asked Feb 14, 2019

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Step 1

- End Behavior:

As the leading term, it means the polynomial which has the highest power of the variable is 2x^{2}, which is an even term, it will always have the positive values for any value of x.

It means that f(x)→∞ as x→ -∞ and f(x)→∞ as x→∞

The graph of the function is shown on the board:

Step 2

- Vertex:

The function is the form of parabola, according its definition it is given as:

y=ax^{2}+bx+c, its vertex is given as x=-b/2a

As the given function is f(x)= 2x^{2}-4x+6,

here a=2, b=-4, c=6

therefore, vertex calculation is shown on the board:

Therefore, the vertex is given for the function is (1,4).

Step 3

- Y-intercept:

y-intercept is a point on the graph where x=0

f(x)= 2x2-4x+6 when x=0

f(x) = 6

So, its y- intercept is (0,6).

- X-intercepts:

x-intercept is a point on the graph where y=0

To determine its intercept we calculate its discriminant, for polynomial function its discriminant is calculated as b2-4ac.

Here, a=2, b=-4, c=6

D= (-4)2-4 X 2 X 6=-32

Discriminant cannot be negative for x € R...

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