document.write( "Question 254208: Find the equation of a quadratic equation if the vertex is (-3, -2) and it passes through the point (-2, 0). \n" ); document.write( "

Algebra.Com's Answer #186586 by drk(1908) $\"\"$ $\"About$

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vertex is (-3, -2) and it passes through the point (-2, 0)
\n" ); document.write( "All parabolas are symmetric, so the other point would be (-4,0).
\n" ); document.write( "We can create a quadratic model based on this using
\n" ); document.write( " $\"Y+=+aX%5E2+%2B+bX+%2B+c\"$
\n" ); document.write( "(i) $\"-2+=+9a+%2B+-3b+%2B+c\"$
\n" ); document.write( "(ii) $\"0+=+4a+-2b+%2B+c\"$
\n" ); document.write( "(iii) $\"0+=+16a+-4b+%2B+c\"$
\n" ); document.write( "eliminate the c from all 3 equations (i) -(ii) to get
\n" ); document.write( "(iv) $\"-2+=+5a+-+b\"$
\n" ); document.write( "and (iii) - (ii) to get
\n" ); document.write( "(v) $\"0+=+12a+-2b\"$
\n" ); document.write( "multiply (iv) by -2 to get
\n" ); document.write( "(vi) $\"4+=+-10a+%2B+2b\"$
\n" ); document.write( "add (v) and (vi) to get
\n" ); document.write( "(vii) $\"4+=+2a\"$
\n" ); document.write( "* a = 2.
\n" ); document.write( "Sub -2 into a for (v) to get
\n" ); document.write( "* b = 12
\n" ); document.write( "Sub values of a and b into (i) to get
\n" ); document.write( "* c = 16
\n" ); document.write( "We get
\n" ); document.write( " y = 2x^2 + 12x + 16 \n" ); document.write( "

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