What is the vertex form of # y= (5x-9)(3x+4)+x^2-4x#?
2 Answers
See below.
Explanation:
First multiply out the brackets and collect like terms:
Bracket terms containing the variable:
Factor out the coefficient of
Add the square of half the coefficient of
Rearrange
Collect like terms:
This is now in vertex form:
Where
So from example:
Explanation:
#"the first step is to rearrange the parabola in standard form"#
#"that is "y=ax^2+bx+cto(a!=0)#
#"expand factors using FOIL and collect like terms"#
#y=15x^2-7x-36+x^2-4x#
#color(white)(y)=16x^2-11x-36larrcolor(red)" in standard form"#
#"the x-coordinate of vertex in standard form is"#
#x_(color(red)"vertex")=-b/(2a)#
#y=16x^2-11x-36#
#"with "a=16,b=-11,c=-36#
#rArrx_(color(red)"vertex")=-(-11)/(32)=11/32#
#"substitute this value into the equation for y"#
#y_(color(red)"vertex")=16(11/2)^2-11(11/32)-36=-2425/64#
#rArrcolor(magenta)"vertex "=(11/32,-2425/64)#
#"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)=(11/32,-2425/64)" and "a=16#
#rArry=16(x-11/32)^2-2425/64larrcolor(red)" in vertex form"#