Table of contents

0. Review of Algebra(0)
1. Equations & Inequalities(0)
2. Graphs of Equations(0)
3. Functions(0)
4. Polynomial Functions(0)
5. Rational Functions(0)
6. Exponential & Logarithmic Functions(0)
7. Systems of Equations & Matrices(0)
8. Conic Sections(0)
9. Sequences, Series, & Induction(0)
10. Combinatorics & Probability(0)

4. Polynomial Functions

Quadratic Functions

4. Polynomial Functions

Quadratic Functions: Study with Video Lessons, Practice Problems & Examples

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23PRACTICE PROBLEM

Consider the quadratic function f(x) = -2x² + 16x - 14 and graph it. With the aid of the graph, identify the largest open intervals within its domain at which it is increasing and decreasing. Also, determine its x and y-intercepts, axis of symmetry, vertex, domain, and range.

ANSWERS OPTIONS

Increasing on (-∞, 4); decreasing on (4, ∞); x-intercepts: (1, 0), (7, 0); y-intercept: (0, -14); axis of symmetry: x = 4; vertex: (4, 18); domain: (-∞, ∞); range: (-∞, 18]

Increasing on (-∞, -4); decreasing on (-4, ∞); x-intercepts: (-7, 0), (-1, 0); y-intercept: (0, -14); axis of symmetry: x = -4; vertex: (-4, 18); domain: (-∞, ∞); range: (-∞, 18]

Increasing on (-∞, 5); decreasing on (5, ∞); x-intercepts: (2, 0), (8, 0); y-intercept: (0, -32); axis of symmetry: x = 5; vertex: (5, 18); domain: (-∞, ∞); range: (-∞, 18]

Increasing on (-∞, -5); decreasing on (-5, ∞); x-intercepts: (-8, 0), (-2, 0); y-intercept: (0, -32); axis of symmetry: x = -5; vertex: (-5, 18); domain: (-∞, ∞); range: (-∞, 18]