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,
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Quadratic Equations and Parabolas
-> 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,
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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):
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 =
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).
