Practice with Parabolas Topic Index | Algebra Index | Regents Exam Prep Center

 Answer the following questions dealing with parabolas.
 1. What is the equation of the axis of symmetry for this parabola? Assume that the turning point (maximum point) is (1,6). Choose: x = 2 x = 1 y = 1 y = 2 Explanation The axis of symmetry passes through the turning point.  It is a vertical line. Its equation is x = 1.

 2. Will the graph of the parabola  y = -2x2 + 4x - 4  open upward or downward? Choose: upward  downward Explanation If the "a" value is negative, it opens downward. Remember, the "a" value is the number in front of x squared.

 3. Which of the following statements is absolutely NOT true for the parabola graphed below. Choose: The x-intercept is (-1,0) The axis of symmetry is y = -1.   The axis of symmetry is x = -1. The "a" coefficient is positive. Explanation The axis of symmetry is a vertical line. The equations of vertical lines read    X =  a number.

 4. What is the equation of the axis of symmetry  of the graph  y = 3x2 + 12x - 2 ? Choose: x = -2 x = 2 y = -2 y = 2 Explanation Remember there is a formula to find this answer without graphing the equation.  Axis of symmetry is x = (-b)/2a.   So for this problem we have x = (-12)/2(3)  =  -2

 5. Which is the equation for the accompanying graph? Choose: y = -x2 - 4 y = -x2 -2x - 4 y = x2- 2x - 3 y = -x2 + 2x + 4 Explanation This parabola opens upward so the "a" coefficient must be positive. That means the number in front of x squared must be a positive number.

 6. What are the roots of this parabola? Choose: 3 and 1 1 and 0 3 and -1 -4 and 0 Explanation The roots are where the parabola crosses the x-axis.  In this graph they are (3,0) and (-1,0).

 7. What is the turning point, or vertex, of the parabola whose equation is y = 3x2 + 6x - 1? Choose: (1,8) (-1,-4) (-3,8) (3,44) Explanation The formula for the axis of symmetry will let you find the vertex. -b/2a = -6/6 = -1 so x = -1. Find the y-value by substituting x = -1 into the equation. y = 3(1) - 6(-1) - 1

 8. For which quadratic equation (parabola) is the axis of symmetry x = 3? Choose: y = -x2 + 3x + 5 y = x2 + 6x + 3 y = -x2 + 6x + 2 y = x2 + x + 3 Explanation Check -b/2a for each equation. The third equation gives 3.

 9. The height, y, in feet, a ball will reach when thrown in the air is given by the equation  y = -16x2 + 30x + 6.  Find to the nearest tenth, the maximum height, in feet, the ball will reach. Choose: 39.3 feet 33.2 feet 20.0 feet 20.1 feet Explanation -b/2a gives -30/-32 for the x-value. Substitute into the equation. y = -16(-30/-32) + 30(-30/-32) + 6

 10. A baseball player throws a ball from the outfield toward home plate.  The ball's height above the ground is modeled by the equation y = -16x2 + 48x + 6, where y represents height, in feet, and x represents time, in seconds.  The ball is initially thrown from a height of 6 feet.  What is the maximum height that the ball reaches? Choose: 76 feet 54 feet 48 feet   42 feet Explanation -b/2a gives -48/-32. Substitute into the equation to find the maximum height y. The fact that it is thrown from 6 feet shows up by the graph crossing the y-axis at 6.

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