HiSET Quadratic Inequalities — practice questions

1. A quadratic equation sets a quadratic expression equal to 0. 2. Replacing the equal sign with an inequality sign gives a quadratic inequality. 3. Its standard form collects everything on one side against 0, as with the equation. 4. The solution is usually an interval or a union of two intervals rather than a short list. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 9.8 Solve Quadratic Inequalities_

1. First find the critical points by solving the related equation set equal to 0. 2. Factoring x squared minus 6x plus 8 gives the brackets (x minus 2) and (x minus 4). 3. So the critical points are x equal to 2 and x equal to 4. 4. The coefficient on the squared term is positive, so the parabola opens upward. 5. An upward parabola is below the x-axis only between its two x-intercepts. 6. The inequality asks where the expression is strictly less than 0, so the interval runs from 2 to 4. 7. The sign is strict, so neither endpoint belongs and both ends take parentheses. 8. The interval [2, 4] wrongly includes the endpoints, where the expression is exactly 0. 9. The interval (0, 8) reads the constant and the middle coefficient as the endpoints. 10. The interval (4, 2) writes the larger number first, but intervals always read left to right. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 9.8 Solve Quadratic Inequalities_

_Source: OpenStax Intermediate Algebra (CC BY 4.0), section 10.3 Evaluate and Graph Logarithmic Functions_