What is the equation of the parabola that has a vertex at # (14, -9) # and passes through point # (0, 2) #?
1 Answer
Aug 25, 2016
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 coordinates of the vertex and a, is a constant.here h = 14 and k = - 9, so we can write a partial equation
#y=a(x-14)^2-9# To find a, substitute the coordinates of (0 ,2) a point on the parabola, into the partial equation.
#rArra(0-14)^2-9=2rArr196a=11rArra=11/196#
#rArry=11/196(x-14)^2-9" is equation in vertex form"# The equation may be expressed in
#color(blue)"standard form"# That is
#y=ax^2+bx+c# by distributing the bracket and simplifying.
#rArry=11/196(x^2-28x+196)-9=11/196x^2-11/7x+2#
graph{11/196(x-14)^2-9 [-20, 20, -10, 10]}
