Determine the quadratic function. Vertex (2,-4) Point: (3,-2). The answer has to be in this format: f(x)=ax^2+bx+c. I'm not sure if I'm right but I have the answer as x^2-4x. Is that right?

1 Answer
Jim G.
Feb 3, 2018

#f(x)=2x^2-8x+4#

Explanation:

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

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))#

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

#"here "(h,k)=(2,-4)#

#rArry=a(x-2)^2-4#

#"to find a substitute "(3,-2)" into the equation"#

#-2=a-4rArra=-2+4=2#

#rArrf(x)=2(x-2)^2-4larrcolor(blue)"in vertex form"#

#"expand factor and collect like terms"#

#f(x)=2(x^2-4x+4)-4#

#color(white)(f(x))=2x^2 -8x+8-4#

#color(white)(f(x))=2x^2-8x+4larrcolor(blue)"in standard form"#

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