Question

question 29 (mandatory) (1 point) ✔ saved which discriminant indicates that a quadratic function has exactly one real solution and the function has one x-intercept? a) $b^2 - 4ac > 0$ b) $b^2 - 4ac = 0$ c) $b^2 - 4ac < 0$ d) $b^2 - 4ac ≠ 0$

Explanation:

To determine the discriminant for a quadratic function \( y = ax^2 + bx + c \) with exactly one real solution and one \( x \)-intercept, we recall the discriminant formula \( D = b^2 - 4ac \):

• If \( b^2 - 4ac>0 \), the quadratic has two distinct real solutions (two \( x \)-intercepts).
• If \( b^2 - 4ac = 0 \), the quadratic has exactly one real solution (a repeated root, so one \( x \)-intercept).
• If \( b^2 - 4ac<0 \), the quadratic has no real solutions (two complex solutions, no \( x \)-intercepts).
• The condition \( b^2 - 4ac

eq0 \) means the discriminant is either positive or negative, so it does not guarantee exactly one real solution.

Thus, the discriminant \( b^2 - 4ac = 0 \) (option b) corresponds to exactly one real solution and one \( x \)-intercept.

Answer:

b) \( b^2 - 4ac = 0 \)