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Nonlinear Equations and Systems Flashcards

7 cards from real Bluebook SAT Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 7 Nonlinear Equations and Systems flashcards as text

  1. Which values of x satisfy x² − x − 12 = 0?

    Answer: x = 4 and x = −3

    Factor: (x−4)(x+3) = 0 → x = 4 or x = −3.

  2. For the equation 3x² − 12x + 12 = 0, what is the value of the discriminant?

    Answer: 0

    Discriminant = (−12)² − 4(3)(12) = 144 − 144 = 0.

  3. Using the quadratic formula, what are the solutions of x² − 6x + 7 = 0?

    Answer: x = 3 ± √2

    x = [6 ± √(36−28)] / 2 = [6 ± √8] / 2 = [6 ± 2√2] / 2 = 3 ± √2.

  4. The system y = x² and y = x + 6 is solved by substitution. What are the x-values of the intersection points?

    Answer: x = 3 and x = −2

    Set x² = x + 6 → x² − x − 6 = 0 → (x−3)(x+2) = 0 → x = 3 or x = −2.

  5. How many points of intersection does the system y = x² − 3 and y = 2x have?

    Answer: 2

    x² − 3 = 2x → x² − 2x − 3 = 0; discriminant = 4 + 12 = 16 > 0, so 2 intersections.

  6. The function f(x) = x² − 4x + 3. At which x-value does f(x) reach its minimum?

    Answer: x = 2

    The vertex x-coordinate = 4 / (2·1) = 2; this is the minimum since a > 0.

  7. The system y = x + 2 and y = x² − 4 has two solutions. What is the sum of their x-coordinates?

    Answer: 1

    x² − 4 = x + 2 → x² − x − 6 = 0; by Vieta's, sum of roots = −(−1)/1 = 1.