document.write( "Question 955395: $\"y=x%5E2%2F16%2B%2821%2F16%29x%2B11%2F8\"$ \r
\n" ); document.write( "\n" ); document.write( "(i) Is the parabola u-shaped or n-shaped? How can you tell this from the equation?\r
\n" ); document.write( "\n" ); document.write( "(ii) Use algebra to find the x-intercepts. \r
\n" ); document.write( "\n" ); document.write( "(iii) Explain why the y-intercept is 11/8\r
\n" ); document.write( "\n" ); document.write( "(iv) Find the equation of the axis of symmetry, explaining your method. Use this information to find the coordinates of the vertex, rounding your answers where necessary to one decimal place. \n" ); document.write( "

Algebra.Com's Answer #583624 by Fombitz(32388) $\"\"$ $\"About$

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(i) Whether the parabola opens upwards (u) or downwards (n) is governed by the sign of the quadratic term's coefficient.
\n" ); document.write( "In this case, $\"1%2F16%3E0\"$ so it opens upwards (u).
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\n" ); document.write( "(ii) To find the x-intercepts, set $\"y=0\"$ and solve for $\"x\"$
\n" ); document.write( " $\"x%5E2%2F16%2B%2821%2F16%29x%2B11%2F8=0\"$
\n" ); document.write( " $\"x%5E2%2B21x%2B22=0\"$
\n" ); document.write( "Complete the square.
\n" ); document.write( " $\"x%5E2%2B21x%2B%2821%2F2%29%5E2%2B22=%2821%2F2%29%5E2\"$
\n" ); document.write( " $\"%28x%2B21%2F2%29%5E2=%28441%2F4%29-88%2F4\"$
\n" ); document.write( " $\"%28x%2B21%2F2%29%5E2=353%2F4\"$
\n" ); document.write( " $\"x%2B21%2F2=0+%2B-+sqrt%28353%29%2F2\"$
\n" ); document.write( " $\"x=-21%2F2+%2B-+sqrt%28353%29%2F2\"$
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\n" ); document.write( "(iii) To find the y-intercept, set $\"x=0\"$ and solve for $\"y\"$
\n" ); document.write( " $\"y=x%5E2%2F16%2B%2821%2F16%29x%2B11%2F8\"$
\n" ); document.write( " $\"y=0%2B0%2B11%2F8\"$
\n" ); document.write( " $\"y=11%2F8\"$
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\n" ); document.write( "(iv) Similar to (ii) complete the square,
\n" ); document.write( " $\"y=x%5E2%2F16%2B%2821%2F16%29x%2B11%2F8\"$
\n" ); document.write( " $\"y=%281%2F16%29%28x%5E2%2B21x%29%2B11%2F8\"$
\n" ); document.write( " $\"y=%281%2F16%29%28x%5E2%2B21x%2B%2821%2F2%29%5E2%29%2B11%2F8-%281%2F16%29%2821%2F2%29%5E2\"$
\n" ); document.write( " $\"y=%281%2F16%29%28x%2B21%2F2%29%5E2%2B88%2F64-441%2F64\"$
\n" ); document.write( " $\"y=%281%2F16%29%28x%2B21%2F2%29%5E2-353%2F64\"$
\n" ); document.write( "So then the vertex occurs at ( $\"-21%2F2\"$ , $\"-353%2F64\"$ ).
\n" ); document.write( "The axis of symmetry is $\"x=-21%2F2\"$ .
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