ALWAYS, SOMETIMES, OR NEVER Chapter 9 Tell whether each statement is always, sometimes, or never true. 1. The graph of a quadratic function is a straight line. 2. The range of a quadratic function is the set of all real numbers. 3. The highest power in a quadratic function is 2. 4. The graph of a quadratic function contains the point (0, 0). 5. The vertex of a parabola occurs at the minimum value of the function. 6. The graph of a quadratic function that has a minimum opens upward. 7. The graphs of f(x) = ax2 and gx= -ax2 have the same width. 8. The function fx= ax2+c has three zeros. 9.
The graph of y= ax2+1 has its vertex at the origin. 10. The graph of y = -x2+c intersects the x-axis. 11. There are two solutions to x2=n when n is positive. 12. If n is a rational number, then the solution to x2=n are rational numbers. 13. If the graph of a quadratic function has its vertex at the origin, then the related quadratic equation has exactly one solution. 14. If the graph of a quadratic function opens upward, then the related quadratic equation has two solutions. 15. If the graph of a quadratic function has its vertex on the x-axis, then the related quadratic equation has exactly one solution. 6. If the graph of a quadratic function has its vertex in the first quadrant, then the related quadratic equation has two solutions. 17. A quadratic equation in the form ax2 – c = 0, where a <0 and c>0 has two solutions. 18. If a quadratic equation has two solutions, then it has two x-intercepts. 19. If the discriminant is equal to zero the quadratic equation has no real solutions. 20. If the leading coefficient of a quadratic equation is positive and the graph of the equation has a positive y-intercept, the graph has two real solutions.
