Here are the essential concepts you must grasp in order to answer the question correctly.
Vertex Form of a Parabola
The vertex form of a parabola is expressed as f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola and 'a' determines the width and direction of the parabola. This form is particularly useful for graphing and understanding the transformations of parabolas.
Recommended video:
Parabola Shape and Coefficient 'a'
The coefficient 'a' in the vertex form affects the shape of the parabola. If 'a' is positive, the parabola opens upwards, while a negative 'a' indicates it opens downwards. The absolute value of 'a' also influences the width; larger values result in a narrower parabola, while smaller values create a wider one.
Recommended video:
Transformations of Functions
Transformations of functions involve shifting, reflecting, stretching, or compressing the graph of a function. In this context, moving the vertex of the parabola to a new point (−10, −5) requires applying a horizontal and vertical shift to the standard form of the parabola, which is essential for writing the equation in vertex form.
Recommended video:
Domain & Range of Transformed Functions