Math Problem Statement

Amati grafik fungsi kuadrat berikut. Apabila fungsi kuadrat tersebut dirotasi 90 derajat searah jarum jam maka koordinat titik balik minimumnya adalah ...

Solution

The question asks to observe the given quadratic function and determine the new coordinates of its minimum point when the graph is rotated 90° clockwise.

Step-by-step explanation:

  1. Identifying the minimum point (vertex):
    From the graph, the quadratic function is a parabola opening upwards. The vertex (minimum point) of the parabola seems to be at approximately (2,4)(-2, -4). This is the original coordinate of the minimum point before rotation.

  2. Rotation by 90° clockwise:
    When rotating a point (x,y)(x, y) by 90° clockwise, the new coordinates can be found by transforming (x,y)(x, y) into (y,x)(y, -x).

    So, applying this to the vertex point (2,4)(-2, -4): (x,y)=(y,x)=(4,2)(x', y') = (y, -x) = (-4, 2)

Thus, after rotating the graph 90° clockwise, the new coordinates of the minimum point are (4,2)(-4, 2).

Would you like further details on how the rotation works, or have any questions? Here are some related questions to consider:

  1. How do you perform rotations by other angles, such as 180° or 270°?
  2. What happens to other points on the graph when rotated by 90°?
  3. Can you find the equation of the new function after the rotation?
  4. How would the graph look after a counterclockwise rotation by 90°?
  5. How does this affect the symmetry of the graph?

Tip: When rotating a point by 90° clockwise, always swap the coordinates and reverse the sign of the original x-coordinate.

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Math Problem Analysis

Mathematical Concepts

Geometry
Rotations
Quadratic Functions

Formulas

(x', y') = (y, -x)

Theorems

Rotation Theorem

Suitable Grade Level

Grades 9-10