SOLUTION: Given the quadratic function f(x) = 2x2� 8x + 11 Use �completing the squares� to convert the quadratic function into vertex form State the vertex, Find the x- and y-intercepts,

Question 1120176: Given the quadratic function f(x) = 2x2� 8x + 11
Use �completing the squares� to convert the quadratic function into vertex form
State the vertex, Find the x- and y-intercepts, Graph the function
the end answer is 2(x-2)^2 +3, I need the steps in-between the problem and the answer
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52754)   (Show Source): You can put this solution on YOUR website!
.

f(x) = 2x^2 - 8x + 11 = 2*(x^2 - 4x) + 11 = 2*(x^2 - 2*2*x + 2^2) - 2*2^2 + 11 = = 2*(x-2)^2 + 3. The vertex is (2,3). The y-intercept is 11. It is the value of f(x) at x= 0. There is no x-intercept: the plot of the function does not intersect x-axis. It is ALWAYS ABOVE the x-axis. Plot y =

Done.

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To see many other similar problems solved by the "completing the square" method and to learn the subject, look into the lesson
    - HOW TO complete the square - Learning by examples
in this site.

Answer by greenestamps(13195)   (Show Source): You can put this solution on YOUR website!

You might want to look at the lesson tutor @ikleyn suggested in her response. Completing the square is a skill you might need in a lot of different types of math problems.

In case they might help your understanding of the process, let me add a few notes of explanation to the solution as she showed it....

Ignore the constant term for the moment; you need to complete the square in the variable x.

To complete the square, you need to factor out the leading coefficient:

Think of the pattern for squaring a binomial: (x+a)^2 = x^2+2ax+a^2. The coefficient of the middle term in the product is twice the constant term in the binomial. So to complete a square you need to take half the coefficient of the linear term and square it.

In this example, the coefficient of the linear term is -4; half of that squared is (-2)^2 = 4. You need to complete the square in the parentheses by adding 4.

Note that you have added 4 inside the parentheses, so you have added 2*4=8 to the expression as a whole. To balance that, you need to subtract 8 from the expression (outside of the parentheses).

Now write the trinomial as a binomial squared, and simplify the rest of the expression.

The square of a number is always 0 or positive, so the minimum value of the expression will be when (x-2) is zero -- i.e., when x=2. And the value of the expression when x=2 is 2(0^2)+3 = 3. So the vertex of the graph is (2,3).
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