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A quadratic function #f(x)=ax^2 +bx +c# , where #a,b and c# are constants, has a minimum point #(2,-13)# and intersects the y-axis at #(0,-5)#

(a) Sketch the graph of the function #f(x)#

(b) Find the function #f(x)# in terms of #x#

1 Answer
Jim G.
Sep 1, 2017

#"see explanation"#

Explanation:

#(a)#

#"we can express f(x) in "color(blue)"vertex form"#

#•color(white)(x)f(x)=a(x-h)^2+k#

#"where "(h,k)" are the coordinates of the vertex and a"#
#"is a constant"#

#"here "(h,k)=(2,-13)#

#rArrf(x)=a(x-2)^2-13#

#"to find a substitute "(0,-5)" into the equation"#

#-5=4a-13rArra=2#

#rArrf(x)=2(x-2)^2-13#

#"since "a>0" then graph is "uuu#

#"plot "(0,-5),(2,-13)#

#"and draw a smooth curve through them"#
graph{2(x-2)^2-13 [-40, 40, -20, 20]}

#(b)#

#f(x)=2(x-2)^2-13#

#color(white)(f(x))=2(x^2-4x+4)-13#

#color(white)(f(x))=2x^2-8x+8-13#

#color(white)(f(x))=2x^2-8x-5larrcolor(red)" in terms of x"#

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