document.write( "Question 1202229: A parabola has x-intercepts 3 and 7 and has vertex (5,2). Determine the equation of this parabola in vertex form. \n" ); document.write( "

Algebra.Com's Answer #836927 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Given the vertex (5,2), the equation in vertex form is of the form

\n" ); document.write( " $\"y=a%28x-5%29%5E2%2B2\"$

\n" ); document.write( "You can use either of the given x-intercepts to determine the value of the constant a.

\n" ); document.write( " $\"0=a%287-5%29%5E2%2B2\"$
\n" ); document.write( " $\"0=4a%2B2\"$
\n" ); document.write( " $\"4a=-2\"$
\n" ); document.write( " $\"a=-1%2F2\"$

\n" ); document.write( "ANSWER: $\"y=%28-1%2F2%29%28x-5%29%5E2%2B2\"$

\n" ); document.write( "When you get familiar with the equations of parabolas, you can determine the constant a without using formal algebra. In this example, the reasoning would go like this:

\n" ); document.write( "From the vertex to either x-intercept, the change in x is 2. If the function were simply y=x^2, then the corresponding change in y would be 2^2=4. But the corresponding change in y in this example is -2; and that means the constant a is -2/4 = -1/2.

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