Burning Up

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.
16. 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 have 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.