Question

Find the vertex of the function given below.
y= 2x2 + 4x + 1

Answer 1

(-1,-1)

Explanation:

To find the x coordinate, we use the formular x = -b/2a where b=4 and a = 2 from the given function.

hence x = -(4)/2(2) = -1

then to get the y coordinate we substitute the value of x into the given function, so y = 2(-1)^2+4(-1)+1 = -1

therefore, the vertex is (-1,-1)

Answer 2

vertex is (-1,-1)

Explanation:

2 ways

1. get into vertex form y=a(x-h)^2+k

2. use math hacks

1.

vertex is (h,k) in y=a(x-h)^2+k

complete square

y=(2x^2+4x)+1

y=2(x^2+2x)+1

y=2(x^2+2x+1-1)+1

y=2((x+1)^2-1)+1

y=2(x+1)^2-2+1

y=2(x+1)^2-1

y=2(x-(-1))^2+(-1)

vertex is (-1,-1)

2.hack way

in form y=ax^2+bx+c

x value of vvertex is -b/2a

given

y=2x^2+4x+1

b=4, a=2

xvaluevertex=-4/(2*2)

xvaluevertex=-4/4=-1

sub back to find y value

y=2(-1)^2+4(-1)+1

y=2(1)-4+1

y=2-4+1

y=-1

y value is -1