Final answer:
The parabola can open either upward or downward depending on the coefficient of the x² term in the equation. The y-intercepts and x-intercepts can be found by setting x = 0 and y = 0 respectively. The axis of symmetry and coordinates of the vertex can be found using formulas.
Step-by-step explanation:
The parabola can open either upward or downward depending on the coefficient of the x² term in the equation of the parabola. If the coefficient is positive, the parabola opens upward, and if the coefficient is negative, the parabola opens downward.
The y-intercept(s) of the parabola can be found by setting x = 0 in the equation and solving for y. These are the points where the parabola intersects the y-axis.
The x-intercepts of the parabola can be found by setting y = 0 in the equation and solving for x. These are the points where the parabola intersects the x-axis.
The axis of symmetry is a vertical line that passes through the vertex of the parabola and divides it into two equal halves. It can be found using the formula x = -b/2a, where a and b are the coefficients of the x² and x terms respectively in the equation of the parabola.
The coordinates of the vertex can be found by substituting the x-value of the axis of symmetry into the equation of the parabola and solving for y.