The equation of the curve is given by y=x^2+ax+3, where a is a constant. Given that this equation can also be written as y=(x+4)^2+b, find (1) the value of a and of b (2) the coordinates of the turning point of the curve Someone can help?

The equation of the curve is given by y=x^2+ax+3, where a is a constant. Given that this equation can also be written as y=(x+4)^2+b, find

(1) the value of a and of b
(2) the coordinates of the turning point of the curve

2 Answers

The explanation is in the images.

Explanation:


Dec 1, 2017

a=8,b=-13,(-4,-13)

Explanation:

x^2+ax+3to(1)

y=(x+4)^2+bto(2)

"expanding "(2)" using FOIL"

y=x^2+8x+16+b

color(blue)"comparing coefficients of like terms"

ax-=8xrArra=8

16+b-=3rArrb=3-16=-13

"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"

y=(x+4)^2-13color(blue)" is in vertex form"

rArrcolor(magenta)"vertex "=(-4,-13)larrcolor(blue)"turning point"