Extra Practice

  1. The factored form of a quadratic equation is y = (2x + 1)(x − 5), and the standard form is y = 2x 2 − 9x − 5. Which of the following statements accurately describes the graph of y ?

    1. The x-intercepts are −1 and 5, and the y-intercept is −5.
    2. The x-intercepts are  and 5, and the y-intercept is −5.
    3. The x-intercepts are  and 5, and the y-intercept is 5.
    4. The x-intercepts are 1 and −5, and the y-intercept is −5.

  2. Taylor fires a toy rocket from ground level. The height of the rocket with respect to time can be represented by a quadratic function. If the toy rocket reaches a maximum height of 34 feet, 3 seconds after it was fired, which of the following functions could represent the height, h, of the rocket t seconds after it was fired?

    1. h(t) = −16(t − 3)2 + 34
    2. h(t) = −16(t + 3)2 + 34
    3. h(t) = 16(t − 3)2 + 34
    4. h(t) = 16(t + 3)2 + 34

  3. If x 2 − 7x = 30 and x > 0, what is the value of x − 5 ?

    1.   5
    2.   6
    3. 10
    4. 25

  4. Which of the following linear expressions divides evenly into 6x 2 + 7x − 20 ?

    1. 3x − 10
    2. 3x − 5
    3. 3x − 4
    4. 3x − 2

  5. If (x, y) is a solution to the system of equations above, what is the value of x 2 ?

    1.   24
    2.   40
    3. 120
    4. 576
  6. A parabola graphed in the first quadrant of a coordinate plane. The graph is titled Tyree’s Punt. Height of Ball in feet is plotted along the vertical axis from zero to 60 in increments of 10. Time in Air in seconds is plotted along the horizontal axis from zero to 4 in increments of point 5. The parabola opens downward, intercepts the Y-axis at zero, has vertex at about 1.85 comma 56, and intercepts the X-axis at zero and again at about 3.7.

    Tyree punts a football into the air. The equation h = −16t 2 + 60t represents the height of the ball in feet, t seconds after it was punted. The graph of part of the equation is shown in the figure above. If Craig punts a ball higher than Tyree did, which of the following equations could be used to find the height of Craig’s punt?

    1. h = −16(t 2 − 3t)
    2. h = −8t(2t − 9)
    3. h = −4(2t − 5)2 + 48
    4. h = −4(2t − 6)2 + 52

  7. If x = −5 when x 2 + 2xk + k2 = 0, what is the value of k ?

    New20SAT20Grid_1.eps

  8. If the graph of y = ax 2 + bx + c passes through the points (−2, −10), (0, 2), and (4, 14), what is the value of a + b + c ?

    New20SAT20Grid_1.eps

  9. Which of the following is equivalent to (2a + 5b)(a − 3b) ?

    1. 2a2 − 2ab − 15b2
    2. 2a2 − ab − 15b2
    3. 2a2 + 2ab − 15b2
    4. 2a2 + 11ab − 15b2

  10. Which of the following are roots of the quadratic equation (x + 3)2 = 49 ?

    1. x = −10, x = 4
    2. x = −10, x = 10
    3. x = −4, x = 10

  11. What information does the value of c reveal when a quadratic equation is written in the form y = ax2 + bx + c, assuming a ≠ 0, b ≠ 0, and c ≠ 0 ?

    1. The solution (zero) of the equation
    2. The location of the graph’s axis of symmetry
    3. The y-intercept of the graph of the equation
    4. The maximum or minimum value of the equation
  12. A parabola graphed on a coordinate plane. The parabola opens downward and has vertex 1.5 comma 12.25. The graph also passes through the following points: negative two comma zero, zero comma 10, three comma 10, and 5 comma zero.

    Which of the following could be the equation of the graph shown?

  13. Which of the following equations has the same solutions as the equation 40 − 6x = x2 ?

    1. y = (x − 6)2 − 40
    2. y = (x − 6)2 + 40
    3. y = (x + 3)2 − 49
    4. y = (x + 3)2 + 49
  14. A parabola graphed on a coordinate plane. The parabola opens upward and passes through the following points: negative one comma two; three-fourths comma zero; zero comma negative three; and one comma zero.

    The following quadratic equations are all representations of the graph above. Which equation directly reveals the exact values of the x-intercepts of the graph?

    1. y = 4x 2 − x − 3
    2. y = (4x + 3)(x − 1)
    3. y = 4(x − 0.125)2 − 3.0625
    4. y + 3.0625 = 4(x − 0.125)2

  15. Given the equation y = −(2x − 4)2 + 7, which of the following statements is not true?

    1. The vertex is (4, 7).
    2. The y-intercept is (0, −9).
    3. The parabola opens downward.
    4. The graph crosses the x-axis at least one time.

  16. The x-coordinates of the solutions to a system of equations are 3.5 and 6. Which of the following could be the system?

  17. What is the positive difference between the roots of the equation  ?

    1. Questions 18-20 refer to the following information.

    2. The following graph shows the paths of two bottle rockets that were fired straight up at the same time. The functions h1(t) and h2(t) represent the heights in feet of the rockets t seconds after they were fired off.

      Two parabolas that open downward graphed on the same coordinate plane. The vertical axis is labeled Height Above Ground, in feet, and the horizontal axis is labeled Time in Air, in seconds. There are no number labels on either axis. Both parabolas start at the origin. The taller parabola is represented by a dashed line and is labeled H sub 2 of T is equal to negative 8 T times the quantity 2 T minus 7. The shorter parabola is represented by a solid line and is labeled H sub 1 of T is equal to negative 16 T times the quantity T minus 3.

    3. After 1 second in the air, how many feet higher was the second bottle rocket than the first?

      New20SAT20Grid_1.eps

    4. How many seconds longer did it take the second rocket to reach its maximum height than the first rocket?

      New20SAT20Grid_1.eps

    5. When written in the form h(t) = −16t 2 + vot + ho, the variable quantities vo and ho represent the initial velocity in feet per second of the rocket and the initial height in feet of the rocket, respectively. How much greater was the initial velocity in feet per second of the second rocket than the first?

      New20SAT20Grid_1.eps

  19. The factored form of a quadratic equation is y = (2x − 3)(x + 5). What are the solutions to the equation?

  20. SAT_C11_HW_Q13.png

    If e is half as far from the origin as f in the figure above, which of the following could be the factored form of the graph’s equation?

    2. y = (x − 1)(x + 2)
    3. y = (x − 1)(2x + 1)
  21. SAT_C11_HW_Q14.png

    If f(x) = ax 2 + bx + c represents the quadratic function whose graph is shown in the figure above, which of the following statements is not true?

    1. a > 0
    2. b > 0
    3. c < 0
    4. All of the statements are true.

  22. Which of the following equations could represent a parabola that has a minimum value of 5 and whose axis of symmetry is the line x = −3 ?

    1. y = (x − 3)2 + 5
    2. y = (x + 3)2 + 5
    3. y = (x − 5)2 + 3
    4. y = (x + 5)2 − 3

  23. If (a, b) and (c, d) represent the solutions to the system of equations above, and a < c, then which of the following statements is true?

    1. a > 0 and c > 0
    2. a < 0 and c < 0
    3. a > 0 and c < 0
    4. a < 0 and c > 0

  24. If the equation of the axis of symmetry of the parabola given by y = 3x 2 + 12x − 8 is x = m, then what is the value of m ?

    1. −8
    2. −4
    3. −2
    4.   0

  25. Given that a, b, and c are all positive integers such that , how many times does the graph of the equation y = ax2 + bx + c cross the x-axis?

    1. 0
    2. 1
    3. 2
    4. There is not enough information to determine how many times the graph crosses the x-axis.

  26. If the quadratic equation y = 3(x + 5)2 + 12 is rewritten in standard form, y = ax2 + bx + c, what is the value of c ?

    New20SAT20Grid_1.eps

  27. If m and n are positive integers where n is 2 less than three times m, and the product of m and n is 176, what is the smaller of the two integers?

    New20SAT20Grid_1.eps
  28. x p(x)
    −2 3
    0 −3
    2 −5
    4 −3
    6 3
    8 13

    The table above shows several points that lie on the graph of quadratic function p(x). Based on the data in the table, what is p(−4) ?

    New20SAT20Grid_1.eps