Two.
It will cross the x-axis twice.
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.
No, it will be entirely above the x-axis if the coefficient of x2 > 0, or entirely below if the coeff is <0.
It will touch it at exactly 1 point. If a quadratic function is given as f(x) = ax2 + bx + c, let the discriminant be denoted as D. Then the graph of y = f(x) will cross the x-axis at the x-values x = (-b + sqrt(D))/(2a) and x = (-b - sqrt(D))/(2a). When the discriminant D = 0, these 2 x-values are actually the same. Thus the graph will touch the x-axis only once.
No. It depends on the function f.
It will cross the x-axis twice.
It will touch the x-axis and not cross it.
Once.
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.
It will touch the x-axis once.
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.
If the discriminant is negative, the equation has no real solution - in the graph, the parabola won't cross the x-axis.
It would not touch or intersect the x-axis at all.
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No, it will be entirely above the x-axis if the coefficient of x2 > 0, or entirely below if the coeff is <0.
0 real solutions. There are other solutions in the complex planes (with i, the imaginary number), but there are no real solutions.
The degree is equal to the maximum number of times the graph can cross a horizontal line.