Question

19)The vertex of the parabola y=x^2+3x+2 lies in Quadrant

1. I
2. II
3. III
4. IV

Answer 1

option 3

Explanation:

Given a parabola in standard form

y = ax² + bx +c ( a ≠ 0 ) , then

the x- coordinate of the vertex is

x = -
`(b)/(2a)`

y = x² + 3x + 2 ← is in standard form

with a = 1, b = 3 , then

x = -
`(3)/(2)`

Substitute this value into the equation for corresponding y- coordinate

y = (-
`(3)/(2)` )² + 3( -
`(3)/(2)` ) + 2 =
`(9)/(4)` -
`(9)/(2)` + 2 = -
`(1)/(4)`

vertex = ( -
`(3)/(2)`, -
`(1)/(4)` ) ← which is in the third quadrant

Answer 2

3.|||

Explanation:

y=x²+3x+2

=x²+3x+9/4-9/4+2

=(x+3/2)²-(9-8)/4

=(x+3/2)²-1/4

put x+3/2=0

x=-3/2

then y=-1/4

so vertex is (-3/2,-1/4)

whiich lies in 3rd quadrant.