Y=2x^2+x+3.
y-intercept?
X-intercept(s)?
Coordinates of the vertex?
Equation of axis of symmetry?
Maximum or minimum?
To find the y-intercept, we set x=0 in the equation:
Y = 2(0)^2 + 0 + 3
Y = 3
Therefore, the y-intercept is at the point (0,3).
To find the x-intercept(s), we set y=0 in the equation and solve for x:
0 = 2x^2 + x + 3
This equation does not have real solutions, indicating that there are no x-intercepts.
The coordinates of the vertex of the parabola can be found using the formula:
x = -b / 2a
x = -1 / (2*2) = -1/4
Substitute x = -1/4 back into the equation to find y:
y = 2(-1/4)^2 + (-1/4) + 3
y = 2(1/16) - 1/4 + 3
y = 1/8 - 1/4 + 3
y = 3 + 1/8
y = 3.125
Therefore, the vertex of the parabola is at (-1/4, 3.125).
The equation of the axis of symmetry is x = -1/4.
Since the coefficient of x^2 is positive (2), the parabola opens upwards. Therefore, the vertex represents the minimum point of the parabola.