Function f is given by #f(x) =x^2#. The graph of f is shifted vertically 3 up, and then scaled vertically by a factor 5. The result is the graph of the function #ax^2+bx+c# with a= 5 b= 0 And c =?

1 Answer
Jim G.
Sep 7, 2017

#c=3#

Explanation:

#"for the parabola in standard form"#

#ax^2+bx+c#

#a" affects the 'openess' of the parabola"#

#"further"#

#•" if "a>0" then graph opens vertically up"#

#• " if "a<0" then graph opens vertically down"#

#b" affects the horizontal position of the vertex"#

#•" if "b>0" then moves to the left by b units"larr#

#• " if "b<0" then moves to the right by b units"rarr#

#c" affects the vertical position of the vertex"#

#• " if "c>0 " then moves vertically up by c units "uarr#

#• " if "c<0" then moves vertically down by c units" darr#

#"in fact c affects all points on the parabola and is"#
#"equivalent to a translation of"#

#((0),(+-c))#

#"here the graph is shifted vertically 3 units up"#

#rArrc=3#
graph{(y-x^2)(y-5x^2-3)=0 [-10, 10, -5, 5]}

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