What is the equation of the parabola that has a vertex at # (-2, -4) # and passes through point # (1,5) #?
1 Answer
Jan 5, 2017
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)=(-2,-4)#
#rArry=a(x-(-2))^2-4#
#rArry=a(x+2)^2-4# To find a, substitute the point (1 ,5) into the equation. That is x = 1 and y = 5
#rArr5=a(1+2)^2-4#
#rArr9a=9rArra=1#
#"Thus " y=(x+2)^2-4color(red)" is equation in vertex form"# Expanding the bracket and simplifying gives.
#y=x^2+4x+4-4#
#rArry=x^2+4xcolor(red)" equation in standard form"#
