Final answer:
A quadratic function in standard form y=ax^2+bx+c has two real zeros if the discriminant, b^2-4ac, is greater than zero.
Step-by-step explanation:
A quadratic function in standard form y = ax^2 + bx + c has two real zeros if the discriminant, which is the expression b^2 - 4ac, is greater than zero. The discriminant determines the nature of the roots. If it is greater than zero, there are two distinct real roots. If it is equal to zero, there is one real root with multiplicity 2. If it is less than zero, there are two complex conjugate roots.
For example, if you have the quadratic function y = x^2 - 4x + 4, you can identify the values of a, b, and c as a = 1, b = -4, and c = 4. The discriminant is calculated as b^2 - 4ac = (-4)^2 - 4(1)(4) = 0. Since the discriminant is zero, the quadratic function has one real root with multiplicity 2 (x = 2).
However, if you have the quadratic function y = x^2 - 4x + 3, the discriminant is calculated as b^2 - 4ac = (-4)^2 - 4(1)(3) = 4. Since the discriminant is greater than zero, the quadratic function has two distinct real roots (x = 1 and x = 3).