Understanding Quadratic Functions | Exploring Coefficients, Shifts, and the Vertex

Quadratic Functions in standard form; f(x)=a(x-h)^2+k

A quadratic function in standard form is represented as:

f(x) = a(x – h)^2 + k

Here is a breakdown of the different elements:

– f(x): This represents the output or value of the function when you input a certain value of x

A quadratic function in standard form is represented as:

f(x) = a(x – h)^2 + k

Here is a breakdown of the different elements:

– f(x): This represents the output or value of the function when you input a certain value of x.

– a: The coefficient “a” represents the stretch or compression of the parabola. If “a” is positive, the parabola opens upwards. If “a” is negative, the parabola opens downwards. The magnitude of “a” determines how wide or narrow the parabola is.

– (x – h): The term (x – h) represents the horizontal shift of the parabola. “h” denotes the horizontal coordinate of the vertex of the parabola.

– k: The term “k” represents the vertical shift of the parabola. If k is positive, the parabola will shift upward, and if k is negative, the parabola will shift downward. “k” denotes the vertical coordinate of the vertex of the parabola.

The vertex of a quadratic function in standard form is located at the point (h, k). The vertex is the highest or lowest point on the graph of the quadratic function, depending on whether “a” is positive or negative.

By analyzing the values of “a,” “h,” and “k,” you can determine the general shape, direction, and position of the parabola on the coordinate plane.

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