Fill in the blank(s) to correctly complete each sentence.
To graph the function ƒ(x) = x² - 3, shift the graph of y = x² down ___ units.

검증된 단계별 안내

Identify the base function and the transformation applied. The base function here is \(y = x^{2}\), which is a standard parabola centered at the origin.

Recognize that the function \(ƒ(x) = x^{2} - 3\) is a vertical shift of the base function \(y = x^{2}\).

Understand that subtracting a constant from the function, as in \(x^{2} - 3\), shifts the graph vertically downward by that constant value.

Therefore, the graph of \(ƒ(x) = x^{2} - 3\) is the graph of \(y = x^{2}\) shifted down by 3 units.

Fill in the blank with the number 3, indicating the downward shift in units.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Graphing Quadratic Functions

Graphing quadratic functions involves plotting parabolas based on the equation y = ax² + bx + c. The basic shape is determined by the coefficient a, while the position is influenced by b and c. Understanding how changes in the equation affect the graph is essential for accurate plotting.

Vertical Shifts of Graphs

A vertical shift moves the entire graph up or down without changing its shape. Adding or subtracting a constant k to the function, as in y = f(x) + k, shifts the graph vertically by k units. Positive k shifts the graph up, while negative k shifts it down.

Interpreting Function Transformations

Function transformations describe how changes to the equation affect the graph's position and shape. Recognizing these transformations, such as shifts, stretches, and reflections, helps in quickly sketching or understanding the graph of modified functions.

Fill in the blank(s) to correctly complete each sentence.To graph the function ƒ(x) = x² - 3, shift the graph of y = x² down ___ units.