Answer:
a. The graph of the quadratic function Y = 2x^2 + 5x - 1 opens upwards and is therefore positive. We know this because the coefficient of the x^2 term, 2, is positive.
b. The graph has a minimum value, since it opens upwards.
c. The equation of the axis of symmetry can be found using the formula x = -b / (2a), where a and b are the coefficients of the x^2 and x terms, respectively. In this case, a = 2 and b = 5, so the equation of the axis of symmetry is x = -5 / (2 * 2) = -5/4.
d. To find the vertex of the parabola, we can substitute the x-coordinate of the axis of symmetry into the equation and solve for y. This gives:
Y = 2(-5/4)^2 + 5(-5/4) - 1 = -9.75
So the vertex is (-5/4, -9.75).
e. To find the y-intercept, we can set x = 0 in the equation and solve for Y:
Y = 2(0)^2 + 5(0) - 1 = -1
So the y-intercept is (0, -1).
Explanation: