Graph each equation. y=-2(x+(1)/(2))^2+6

Name: Problem 25, Chapter 10: Intermediate Algebra for College Students
Uploaded: 2020-03-24T23:30:59-08:00
Duration: 1 min 21 s
Channel: Joshua Eastwood
Description: Graph each equation. y=-2(x+(1)/(2))^2+6

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Key Concepts

Parabolic Graph

A parabola is the curve defined by a quadratic function. Its shape is characterized by a symmetric, U-shaped graph that opens upward when the leading coefficient is positive or downward when it is negative. The curvature and direction are key to understanding the graph of a quadratic function.

Axis of Symmetry

The axis of symmetry is a vertical line that runs through the vertex of a parabola, effectively dividing it into two mirror-image halves. This line is important because it helps in locating the vertex and understanding the balance of the quadratic curve.

Vertex Form of a Quadratic Function

The vertex form, expressed as y = a(x - h)^2 + k, clearly shows the vertex (h, k) of the parabola, which is the turning point of the function. This form makes it straightforward to identify key features like the vertex, axis of symmetry, and the direction in which the parabola opens.

Function Transformations

Graphing a quadratic function using the vertex form involves several transformations. These include horizontal and vertical shifts, which move the graph from the origin to a new position, as well as reflections and vertical stretching or compressing, which alter the shape and orientation of the parabola.

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