What is the vertex form of y=x^2+14x+3 y=x2+14x+3?

2 Answers
Harish Chandra Rajpoot
Jul 22, 2018

(x+7)^2=y+46(x+7)2=y+46

Explanation:

Given equation:

y=x^2+14x+3y=x2+14x+3

y=x^2+2(7)x+7^2-7^2+3y=x2+2(7)x+72−72+3

y=(x+7)^2-46y=(x+7)2−46

(x+7)^2=y+46(x+7)2=y+46

The above equation is in vertex form of upward parabola: (x-x_1)^2=4a(y-y_1)(x−x1)2=4a(y−y1)

The vertex of parabola :(x-x_1=0, y-y_1=0)(x−x1=0,y−y1=0)

(x+7=0, y+46=0)\equiv(-7, -46)(x+7=0,y+46=0)≡(−7,−46)

Jim G.
Jul 22, 2018

y=(x+7)^2-46y=(x+7)2−46

Explanation:

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

•color(white)(x)y=a(x-h)^2+k∙xy=a(x−h)2+k

"where "(h,k)" are the coordinates of the vertex and a"where (h,k) are the coordinates of the vertex and a
"is a multiplier"is a multiplier

"to obtain this form "color(blue)"complete the square"to obtain this form complete the square

y=x^2+2(7)x+49-49+3y=x2+2(7)x+49−49+3

y=(x+7)^2-46larrcolor(red)"in vertex form"y=(x+7)2−46←in vertex form

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