Algebra 2 Systems of Linear and Quadratic Equations Quiz: 10 Questions with Explanations

A Only 2B 0, 1, or 2C 1 or 2D 0, 1, 2, or 3

After substitution you get a quadratic, which has 0, 1, or 2 real solutions.

A \((2, 4)\)B \((4, 2) and (-4, 2)\)C \((16, 4)\)D \((2, 4) and (-2, 4)\)

x² = 4 gives x = ±2, and y = 4 for both.

A The left panelB The right panelC All of themD The middle panel

A tangent line meets the parabola at exactly one point, which happens when D = 0.

A \(x^{2} + x + 2 = 0\)B \(x^{2} – x + 2 = 0\)C \(x^{2} – x – 2 = 0\)D \(x^{2} = 2\)

x² = x + 2 becomes x² – x – 2 = 0.

A \((-2, 3) and (4, 9)\)B \((-2, 4) and (3, 9)\)C \(x = -2 and x = 3\)D \((2, 4) and (-3, 9)\)

Intersection points are ordered pairs: (-2, 4) and (3, 9).

A two real solutionsB one real solutionC no real solutionsD infinitely many solutions

x² – 3x + 4 = 0 has D = 9 – 16 = -7 < 0, so the line misses the parabola.

A \((2, 3)\)B \((3, 2)\)C \((2, 1)\)D \((-2, -3)\)

Check (2, 3): 4 + 9 = 13 and 2(2) – 1 = 3. For (3, 2), 2(3) – 1 = 5, not 2.

A \(D = 0\)B \(D > 0\)C \(D < 0\)D \(D = 1\)

D = 0 gives exactly one solution, so the line touches the parabola once.

A 0B 2C 1D 4

The graph shows the line crossing the circle twice, at (3, 4) and (-4, -3).

A 4 and 6B 3 and 8C 2 and 12D 5 and 5

x + y = 10 and xy = 24 gives x = 4, y = 6 (or 6 and 4).