If you mean: 3x2+8+5 = 0
Then it crosses the x axis at points -1 and -5/3
It will touch it once.
Once.
Once and the roots are said to be equal.
y=1 does not cross the x-axis. It is a line parallel to the x-axis (and therefore can't ever cross it)
A graph of an equation in the form y = ax^2 + bx + c will cross the y-axis once - whatever its discriminant may be.
It will cross the x-axis twice.
It would not touch or intersect the x-axis at all.
It will touch it once.
Once.
Once and the roots are said to be equal.
It doesn't cross the x-axis since the position the equation is in is 9 units above the x-axis and the graph never curves the other way so it will never touch the x-axis
y=1 does not cross the x-axis. It is a line parallel to the x-axis (and therefore can't ever cross it)
A graph of an equation in the form y = ax^2 + bx + c will cross the y-axis once - whatever its discriminant may be.
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.
Discriminant = 116; Graph crosses the x-axis two times
0 real solutions. There are other solutions in the complex planes (with i, the imaginary number), but there are no real solutions.
Without knowing the plus or minus value of 40 it's difficult to say but in general:- If the discriminant of a quadratic equation = 0 then it touches the x axis at 1 point If the discriminant is greater than zero then it touches the x axis at 2 points If the discriminant is less than zero then it does not touch the x axis