How do you write f(x) = x^2+7x+10f(x)=x2+7x+10 in vertex form?

1 Answer
Jim G.
Aug 6, 2017

y=(x+7/2)^2-9/4y=(x+72)2−94

Explanation:

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

"for a parabola in standard form "y=ax^2+bx+c

x_(color(red)"vertex")=-b/(2a)

y=x^2+7x+10" is in standard form"

"with "a=1,b=7,c=10

rArrx_(color(red)"vertex")=-7/2

"substitute this value into f(x) for y-coordinate"

y_(color(red)"vertex")=(-7/2)^2+(7xx-7/2)+10=-9/4

rArrcolor(magenta)"vertex "=(-7/2,-9/4)

rArry=(x+7/2)^2-9/4larrcolor(red)" in vertex form"

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