Given that f is a quadratic function with maximum f(x)=f(-3)=-5, find the axis, vertex, range, a

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Given that f is a quadratic function with maximum...

Key Concepts

x-intercepts (Roots/Zeros)

The x-intercepts of a quadratic function are the points where the function crosses the x-axis, corresponding to the solutions of the equation f(x) = 0. These intercepts can be found by techniques such as factoring, completing the square, or using the quadratic formula, and they provide valuable information about the behavior of the function.

Axis of Symmetry

The axis of symmetry is a vertical line that passes through the vertex of a quadratic function, effectively dividing the parabola into two mirror-image halves. It is given by the line x = -b/(2a) when the function is in standard form, and it plays a crucial role in understanding the structure and balance of the function's graph.

Range

The range of a quadratic function is the set of y-values that the function can take. Depending on whether the parabola opens upward or downward, the range is determined by the y-coordinate of the vertex. This concept is important for understanding the limits of the function’s output.

Quadratic Function

A quadratic function is a polynomial of degree two, typically expressed in the form ax² + bx + c, where a, b, and c are constants and a ? 0. Its graph is a parabola that opens upward or downward depending on the sign of a, and its fundamental properties such as symmetry and vertex are key to understanding its behavior.

Vertex

The vertex of a quadratic function is the single point where the function reaches its maximum or minimum value. In a parabola, it is the point of turning, and when the function is written in vertex form, it clearly indicates the coordinates of this point. Understanding the vertex is essential for graphing and analyzing the function.

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