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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. For the quadratic f(x) = 2x² − 8x + 6, what are the x-intercepts?

    Answer: x = 1 and x = 3

    2x² − 8x + 6 = 2(x² − 4x + 3) = 2(x − 1)(x − 3); x-intercepts at x = 1 and x = 3.

  2. Solve: x² − 81 = 0

    Answer: x = ±9

    x² = 81; x = ±9.

  3. The system y = 2x − 1 and y = x² − 4x + 3 is solved. What is the product of the x-coordinates of the solutions?

    Answer: 4

    2x − 1 = x² − 4x + 3 → x² − 6x + 4 = 0; by Vieta's, product of roots = c/a = 4.

  4. A quadratic has a positive leading coefficient and vertex at (2, −3). How many x-intercepts does it have?

    Answer: 2

    The parabola opens upward (positive leading coefficient) and its minimum is −3 < 0; it must cross the x-axis twice.

  5. If x² + 12x + c = (x + 6)², what is the value of c?

    Answer: 36

    (x + 6)² = x² + 12x + 36, so c = 36.

  6. The equation 5x² = 3x has a non-zero solution. What is it?

    Answer: x = 3/5

    5x² − 3x = 0 → x(5x − 3) = 0; solutions are x = 0 and x = 3/5; the non-zero solution is x = 3/5.

  7. The parabola y = x² − 4x + 3 is shifted 2 units to the right. What is the new equation?

    Answer: y = x² − 8x + 15

    Shifting right by 2 replaces x with (x − 2): y = (x−2)² − 4(x−2) + 3 = x² − 4x + 4 − 4x + 8 + 3 = x² − 8x + 15.