document.write( "Question 915298: The Pedestrian Bridge over the Yarra River is a bow truss construction and the curve of the arch is a parabola. The length of the bridge is 45.7 metres and the height of the arch is 10.65 metres. The rule I was given is y=a(x+h)²+k. \r
\n" ); document.write( "\n" ); document.write( "What is the value of a, h and k? \r
\n" ); document.write( "\n" ); document.write( "How would I draw this parabola on a graph?\r
\n" ); document.write( "\n" ); document.write( "Thanks \n" ); document.write( "
Algebra.Com's Answer #555542 by rothauserc(4718)\"\" \"About 
You can put this solution on YOUR website!
The general formula of a parabola is given by your example (note (x-h) NOT (x+h),
\n" ); document.write( "y = a(x-h)^2 + k where the point (h,k) is the vertex
\n" ); document.write( "we are given the length of the bridge is 45.7 m and height is 10.65, therefore
\n" ); document.write( "h = 45.7/2 = 22.85
\n" ); document.write( "k = 10.65
\n" ); document.write( "so far we have
\n" ); document.write( "y = a(x-22.85)^2 + 10.65
\n" ); document.write( "we have two x intercepts, (0,0) and (45.7, 0)
\n" ); document.write( "let's use (0,0) to find our value for a
\n" ); document.write( "0 = a(0-22.85)^2 +10.65
\n" ); document.write( "0 = a522.1225 +10.65
\n" ); document.write( "a522.1225 = -10.65
\n" ); document.write( "a = -10.65 / 522.1225 = −0.020397512 which is approx -0.02
\n" ); document.write( "now we have
\n" ); document.write( "y = -0.02(x-22.85)^2 + 10.65
\n" ); document.write( "y = -0.02x^2 +0.02*45.7x + -0.02*522.1225
\n" ); document.write( "y = -0.02x^2 +0.914x -10.44245 +10.65
\n" ); document.write( "y = -0.02x^2 +0.914x +0.20755
\n" ); document.write( "it's graph looks like
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-60%2C+60%2C+-10%2C+20%2C+-0.02x%5E2+%2B0.914x+%2B0.20755+%29+\"\r
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