Prove that the vertex of parabola y=x^2+5x+1 is in third quadrant.
To prove that the coordinates of a point are located in the 3rd quadrant of Cartesian coordinate system, we'll have demonstrate that both their values are negative.
We'll calculate the vertex of the parabola using the formula:
V(-b/2a ; -`Delta` /4a),
`Delta` = b^2 - 4ac
a,b,c are the coefficients of quadratic:
a=1, b=5 and c=1.
`Delta` = 25 - 4 = 21
-b/2a = -5/2
-`Delta` /4a = -21/4
Since the x and y coordinates of the vertex of parabola are negative, the vertex V(-5/2 ; -21/4) is located in the 3rd quadrant of Cartesian coordinate system.