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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. Using the quadratic formula, what are the solutions to 2x² − 4x − 6 = 0?

    Answer: x = 3 and x = −1

    Divide by 2: x² − 2x − 3 = 0 → (x−3)(x+1) = 0 → x = 3 or x = −1.

  2. The parabola y = (x − 3)² − 4 intersects the x-axis at which two values of x?

    Answer: x = 1 and x = 5

    Set y = 0: (x−3)² = 4 → x−3 = ±2 → x = 5 or x = 1.

  3. How many solutions does the system y = x² + 3x + 2 and y = x + 2 have?

    Answer: 2

    x² + 3x + 2 = x + 2 → x² + 2x = 0 → x(x+2) = 0 → x = 0 or x = −2; two solutions.

  4. The equation x² + px + 16 = 0 has two equal real roots. What is the positive value of p?

    Answer: 8

    Equal roots require discriminant = 0: p² − 64 = 0 → p = ±8; the positive value is 8.

  5. A parabola y = x² − 4x + c does not intersect the x-axis. Which value of c satisfies this condition?

    Answer: c = 5

    Discriminant 4; only c = 5 satisfies this.

  6. If x² − 7x + 10 = 0, what is the value of x² − 7x?

    Answer: −10

    From the equation: x² − 7x + 10 = 0 → x² − 7x = −10.

  7. Which of the following systems has exactly one solution?

    Answer: y = (x−1)² and y = 0

    (x−1)² = 0 → x = 1 is the only solution; all other choices yield 0 or 2 solutions.