In Exercises 9–16, find the coordinates of the vertex for the par...

Question

In Exercises 9–16, find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=2x^2−8x+3

Accepted Answer

Hey everyone here we are asked to find the vertex of the parabola which is F of X is equal to three, X squared minus 30 X plus 79. Now to find the vertex from this equation we have to convert it to vertex form. So if you recall vertex form for a parabola is F of X is equal to a times the quantity of X minus H squared plus K. And now from here to convert our given equation we have to complete the square. But first we need to notice that our x squared term has a coefficient. So we need to factor this three out of both of the X terms. So we have three times the quantity of X squared minus 10 X and plus 79. So from here if we recall we can start completing the square by taking the coefficient of this X and dividing it by two. So we have negative 10 divided by two and then squaring that term. So negative 10 divided by two, two is negative five squared gives us 25. So now we know we need to act 25 within these parentheses. So we have three times the quantity of X squared minus X plus 25 plus 79. But since we added 25 within the parentheses we have to subtract the same quantity from the entire equation. So we can't just subtract 25, we have to multiply it by this three which we factored out earlier. So we are really subtracting 25 times three. So now our equation is three times the quantity of x squared minus 10 X plus 25 plus minus 75. And now to finish completing the square, we have to rewrite this trin Amiel as a square. So we now have three times the quantity of x minus five Squared plus -75 is just four. So now we finally have our equation converted into vertex form. So we need to recall that a vertex uses the variables H&K. So with this information we can start comparing our equation to the formula. So we can notice that our H is minus five and while H is also negative in the formula, so our H point is just positive five and now our K. Is positive four. Well K is positive in the formula as well. So our K point is positive for Therefore we are left with answer choice B with a vertex of 54. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

In Exercises 9–16, find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=2x^2−8x+3

Key Concepts

Quadratic Functions

Vertex of a Parabola

Completing the Square

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