It is the axis of symmetry.
The real solutions are the points at which the graph of the function crosses the x-axis. If the graph never crosses the x-axis, then the solutions are imaginary.
Once.
...i need the answer to that too...
If the discriminant is negative, the equation has no real solution - in the graph, the parabola won't cross the x-axis.
Yes it is possible. The solutions for a quadratic equation are the points where the function's graph touch the x-axis. There could be 2 places to that even if the graph looks different.
The real solutions are the points at which the graph of the function crosses the x-axis. If the graph never crosses the x-axis, then the solutions are imaginary.
The zeros of a quadratic function, if they exist, are the values of the variable at which the graph crosses the horizontal axis.
When the graph of a quadratic crosses the x-axis twice it means that the quadratic has two real roots. If the graph touches the x-axis at one point the quadratic has 1 repeated root. If the graph does not touch nor cross the x-axis, then the quadratic has no real roots, but it does have 2 complex roots.
Two.
It will cross the x-axis twice.
It will touch the x-axis and not cross it.
It will touch the x-axis once.
Once.
It would not touch or intersect the x-axis at all.
If the quadratic function is written as ax2 + bx + c then if a > 0 the function is cup shaped and if a < 0 it is cap shaped. (if a = 0 it is not a quadratic) if b2 > 4ac then the equation crosses the x-axis twice. if b2 = 4ac then the equation touches the x-axis (is a tangent to it). if b2 < 4ac then the equation does not cross the x-axis.
...i need the answer to that too...
If the discriminant is negative, the equation has no real solution - in the graph, the parabola won't cross the x-axis.