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.
The number of solutions for a quadratic equation corresponds to the points where the graph of the quadratic function intersects the x-axis. If the graph touches the x-axis at one point, the equation has one solution (a double root). If it intersects at two points, there are two distinct solutions, while if the graph does not touch or cross the x-axis, the equation has no real solutions. This relationship is often analyzed using the discriminant from the quadratic formula: if the discriminant is positive, there are two solutions; if zero, one solution; and if negative, no real solutions.
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.