document.write( "Question 625231: f(x)=1/2(x+9)^2+7\r
\n" ); document.write( "\n" ); document.write( "I got 95/2 but I am confused because I have never run into a problem with no x-intercept. So how do I write an ordered pair for the vertex? \n" ); document.write( "

Algebra.Com's Answer #393388 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"f%28x%29=%281%2F2%29%28x%2B9%29%5E2%2B7+\"$ is a quadratic function.
\n" ); document.write( "As such, its graph is a parabola.
\n" ); document.write( "Unlike linear functions, which graph as straight lines, quadratic functions are allowed to have no x-intercept.
\n" ); document.write( "They may approach the x-axis for a while, but then they change their mind and turn away from the x-axis, never crossing it.
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\n" ); document.write( "For your function:
\n" ); document.write( " $\"f%28x%29=7\"$ for $\"x=-9\"$
\n" ); document.write( "For any other value of x,
\n" ); document.write( " $\"%28x%2B9%29%5E2%3E0\"$ and $\"f%28x%29%3E7\"$
\n" ); document.write( "There is no x-intercept, because $\"f%28x%29%3E=7\"$ for all values of x.
\n" ); document.write( "The graph never crosses the x-axis (the y=0 line), because $\"f%28x%29\"$ is never zero.
\n" ); document.write( "The function has a minimum at $\"x=-9\"$ with $\"f%28-9%29=7\"$
\n" ); document.write( "The vertex of the parabola is at that point: point(-9,7).
\n" ); document.write( "Your function graphs as this:
\n" ); document.write( " $\"graph%28300%2C300%2C-18%2C2%2C-5%2C45%2C%28x%2B9%29%5E2%2F2%2B7%29\"$
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\n" ); document.write( "Quadratic functions can be written in the form
\n" ); document.write( " $\"f%28x%29=a%28x-h%29%5E2%2Bk\"$ or $\"y=a%28x-h%29%5E2%2Bk\"$
\n" ); document.write( "with $\"a\"$ , $\"h\"$ , and $\"k\"$ being some real numbers (and a must not be zero).
\n" ); document.write( "When written in that form, (h,k) is the vertex, and $\"a\"$ tells you how curvy the curve is and which way it goes.
\n" ); document.write( "The larger the absolute value of $\"a\"$ , the curvier the curve is.
\n" ); document.write( "If $\"a\"$ is positive, the curve goes up from the vertex on both sides, as $\"%28x-h%29%5E2\"$ gets larger and larger. It looks like a smiley mouth.
\n" ); document.write( "If $\"a\"$ is negative, the curve goes down from the vertex on both sides, as $\"%28x-h%29%5E2\"$ gets larger and larger. It's frowning.
\n" ); document.write( "Your curve is smiling at you. \n" ); document.write( "

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