document.write( "Question 148160: Consider the Function $\"f%28x%29=x%5E2%2B6x-2\"$ Part A. Find h, the x-coordinate of the vertex of this parabola (show work) Part B. Substitute the two integers immediately to the right of the h into the function to find the corresponding y values. Fill in a table and make sure your x-values are in increasing order in your table. \n" ); document.write( "

Algebra.Com's Answer #108560 by nabla(475) $\"\"$ $\"About$

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A. There really isn't much work to show. You are applying the simple rule:
\n" ); document.write( "x=-b/(2a) is the vertex of a parabola in form f(x)=ax^2+bx+c. I will derive this for you after we apply the rule.\r
\n" ); document.write( "\n" ); document.write( "For f(x)=x^2+6x-2,
\n" ); document.write( "x=-6/2=-3 will be the x-coordinate of the vertex.\r
\n" ); document.write( "\n" ); document.write( "Derivation:
\n" ); document.write( "consider the derivative of the function, f'(x).
\n" ); document.write( "f'(x)=2x+6. For a quadratic equation, wherever the derivative is zero, we shall have a minimum or maximum, which by definition follows as the vertex.
\n" ); document.write( "So 0=2x+6, or x=-3. This is obviously the same answer we got from the rule, because it uses the same method:
\n" ); document.write( "f(x)=ax^2+bx+c
\n" ); document.write( "f'(x)=2ax+b
\n" ); document.write( "0=2ax+b
\n" ); document.write( "x=-b/(2a).\r
\n" ); document.write( "\n" ); document.write( "B. I'm not entirely certain what is wanted... f(-2) and f(-1)???
\n" ); document.write( "Just plug in the values into the equation and find the values. You can make a simple table likewise. \n" ); document.write( "

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