document.write( "Question 450628: Find the vertex, the line of symetry, and the maximum/minimum value of f(x). Graphe the function. f(x)=1/4(x+3)^2+7. Is the value f(-3)=7 a minimum or a maximum \n" ); document.write( "

Algebra.Com's Answer #309971 by htmentor(1343) $\"\"$ $\"About$

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Putting the quadratic in standard form gives:
\n" ); document.write( "f(x) = 1/4(x^2+6x+9) + 7 = 1/4x^2 + 3/2x + 37/4
\n" ); document.write( "The x-value of the vertex is -b/2a = (-3/2)/(2/4) = -3
\n" ); document.write( "Substitute this value into the original equation to get the y-value of the vertex:
\n" ); document.write( "f(x) = y = 1/4(0)^2 + 7 = 7
\n" ); document.write( "So the vertex is (-3,7)
\n" ); document.write( "The line of symmetry is the vertical line which passes through the vertex:
\n" ); document.write( "x = -3
\n" ); document.write( "The parabola opens upward so the maximum value is f(x) = $\"infinity\"$
\n" ); document.write( "The minimum value is the y-value of the vertex: f(x) = 7
\n" ); document.write( " $\"graph%28400%2C400%2C-20%2C20%2C-30%2C30%2C1%2F4%2A%28x%2B3%29%5E2%2B7%29\"$ \n" ); document.write( "

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