What is the equation of the parabola that has a vertex at # (1, 8) # and passes through point # (5,44) #?

1 Answer
Jim G.
May 9, 2016

#y=9/4(x-1)^2+8#

Explanation:

The equation of a parabola in #color(blue)" vertex form ""is"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(y=a(x-h)^2+k)color(white)(a/a)|)))#
where (h ,k) are the coords of vertex

here the vertex = (1 ,8) and so

#y=a(x-1)^2+8#

now (5 ,44) lies on the parabola and therefore will satisfy the equation.
Substituting x = 5 , y = 44 into the equation allows us to find a.

#44=a(5-1)^2+8→ 16a=36rArra=9/4#

equation of parabola is : #y=9/4(x-1)^2+8#

or in standard form- obtained by expanding bracket , we also get

#y=9/4x^2-9/2x+41/4#

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