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)=−x^2−2x+8

Accepted Answer

hey everyone here we are asked to find the vertex of the parabola which is F of X is equal to negative two, X squared minus four X plus three. And now here we to vertex we have to convert our given equation into vertex form. So we need to recall that the 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 to convert our given equation we're going to have to complete the square. So we want to look at these X terms here and we need to notice that our squared X term has a coefficient. So we need to factor it out from both. X is so we have negative two times the quantity of X squared plus two X and plus three which is outside of the parentheses. And now if you recall we you can start completing the square by taking the coefficient of the X term and dividing it by two and then squaring that quantity. So we have two divided by two, which is just one squared, which gives us one. So now we know we need to add one inside the set of parentheses. So we have negative two times the quantity of X squared plus two X plus one and plus three. But since we added one in the inside of the parentheses we have to subtract that same quantity from the entire equation. So we can't just subtract one, we have to multiply it by this negative two which we factored out earlier. So we really have to subtract negative two times one which is negative two. So now our equation is negative two times the quantity of x squared plus two X plus one plus three minus negative two which is plus two. Now to finish completing the square we have to rewrite this trin Amiel as a square. So we have negative two times the quantity of X plus one squared plus three plus two which is plus five. And now we can see that our original equation is now in vertex form and we just need to recall that a vertex is the point H. K. So we now can compare our equation to the vertex form of a parabola. So we see that our K term is positive just like it is in the formula. So our k term is just positive five but our each term is positive but it is negative in the formula. So our H term is negative one. Therefore our answer here is choice B. With a vertex of negative 15. 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)=−x^2−2x+8

Key Concepts

Quadratic Functions

Vertex of a Parabola

Completing the Square

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