How do you write a quadratic equation with y-intercept of -4 and vertex at (3, -7)?

1 Answer
Jim G.
May 3, 2017

#y=1/3x^2-2x-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 constant.

#"here " (h,k)=(3,-7)#

#rArry=a(x-3)^2-7#

#"to find a, use y-intercept of - 4"rarr(0,-4)#

#-4=9a-7#

#rArra=1/3#

#rArry=1/3(x-3)^2-7larrcolor(red)" in vertex form"#

#"distributing and simplifying gives"#

#y=1/3(x^2-6x+9)-7#

#rArry=1/3x^2-2x-4larrcolor(red)" in standard form"#

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