Table of contents

0. Review of Algebra4h 16m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 19m
10. Combinatorics & Probability1h 45m

4. Polynomial Functions

Quadratic Functions

College Algebra

4. Polynomial Functions

Quadratic Functions

1:12 minutes

Problem 3d

Textbook Question

Fill in the blank(s) to correctly complete each sentence. The highest point on the graph of a parabola that opens down is the ____ of the parabola.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Parabola

A parabola is a symmetrical, U-shaped curve that can open either upwards or downwards. It is defined by a quadratic function of the form y = ax^2 + bx + c, where 'a' determines the direction of the opening. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

Vertex

The vertex of a parabola is the highest or lowest point on its graph, depending on the direction it opens. For a parabola that opens downwards, the vertex represents the maximum point. The coordinates of the vertex can be found using the formula (-b/2a, f(-b/2a)) for the quadratic function.

Maximum and Minimum Values

In the context of parabolas, the maximum value occurs at the vertex for parabolas that open downwards, while the minimum value occurs at the vertex for those that open upwards. Understanding these values is crucial for analyzing the behavior of quadratic functions and their graphs.