Algebra 1 Solving Quadratic Equations Quiz: 10 Questions with Explanations

A \(x = 6\) or \(x = -6\)B \(x = 6\)C \(x = 18\)D \(x = -6\)

Both 6 and -6 square to 36. Taking only the positive root misses a solution.

A \(x = -1\) or \(x = 5\)B \(x = 1\) or \(x = -5\)C \(x = -1\) or \(x = -5\)D \(x = 1\) or \(x = 5\)

Set each factor to 0: x + 1 = 0 gives -1, and x – 5 = 0 gives 5.

A \(x = 0\) and \(x = 3\)B \(x = 1\) and \(x = 3\)C \(x = -1\) and \(x = -3\)D \(x = 3\) only

The solutions are the x-intercepts of the parabola.

A \(x = -3\) or \(x = -8\)B \(x = 4\) or \(x = 6\)C \(x = 3\) or \(x = -8\)D \(x = 3\) or \(x = 8\)

The numbers 3 and 8 have product 24 and sum 11, so (x – 3)(x – 8) = 0.

A 9B 6C 3D 36

Half of -6 is -3, and (-3)² = 9, so the trinomial is (x – 3)².

A 4B 36C -4D -36

b² – 4ac = 16 – 20 = -4, so there are no real solutions.

A OneB TwoC NoneD Four

A positive discriminant gives two different real solutions.

A \(x = 1 \pm \sqrt{2}\)B \(x = -2 \pm \sqrt{2}\)C \(x = -1 \pm \sqrt{2}\)D \(x = -1 \pm 2\)

x = (-2 ± √(4 + 4))/2 = (-2 ± 2√2)/2 = -1 ± √2.

A 8 feetB 6 feetC 4 feetD 24 feet

w(w + 2) = 48 gives w² + 2w – 48 = 0, so (w + 8)(w – 6) = 0. The width must be positive: 6 ft.

A 1 secondB 16 secondsC 4 secondsD 2 seconds

Factor: -16t(t – 2) = 0, so t = 0 or t = 2. The ball lands at 2 seconds.