How can you tell from the standard form whether a quadratic function has exactly one zero

The discriminant equals zero.

Explanation:

The standard form of a quadratic equation is

ax² + bx + c = 0

The solution is the familiar quadratic formula

The term b² -4ac is the discriminant (D).

D tells you the number of roots.

If D = 0, the solution to the equation becomes

If D = 0, there is exactly one zero.

===============

Example:

Find the zeroes of

f(x) = x² - 2x + 1

x = 1

The graph is a parabola with its vertex touching the x-axis at x = 1.

you didn't give me the choices, so i will just give you the graph so you can look at your choices and choose the right one.