Quadratic Equations with One Solution Practice Test

Work with repeated roots, perfect-square trinomials, tangent parabolas, and discriminant-zero parameter values.

Quadratic Equations with One Solution Practice Test

This test has 20 questions

About This One Solution Practice Test

This test isolates the repeated-root case. Questions connect D=0, perfect-square trinomials, a vertex on the x-axis, and a parabola tangent to the axis.

Parameter questions require solving the exact equality that makes two quadratic-formula branches coincide.

Skills Covered

Repeated roots, perfect squares, zero discriminants, tangency, vertex form, and parameter conditions.

Key Ideas

  1. A repeated root is one distinct solution with multiplicity two.
  2. D=0 is an equality, not an interval.
  3. A tangent point is the vertex when the vertex lies on y=0.
  4. Factor signs reverse when converted to roots.

Common Mistakes to Avoid

Do not write ± when the square equals zero, and do not count a repeated root as two distinct real solutions.

Practice Format

Each question has four answer choices. The explanation shows the method, completes the algebra, states the conclusion, and explains why every distractor is incorrect.