![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
It is known that the line y = 1 / 2x + 3 intersects the two coordinate axes at two points a and B. the image of the quadratic function y = - x ^ 2 / 4 is translated left and right first, and then up and down twice, so that it passes through points a and B to find the vertex coordinates of the translated image
For the line y = 1 / 2x + 3, when x = 0, y = 3, the intersection coordinates of the line and Y axis are (0,3) when y = 0, 1 / 2x + 3 = 0, x = - 6, the intersection coordinates of the line and X axis are (- 6,0), the vertex coordinates of the quadratic function y = - X & # 178 / 4 are (0,0). Let the quadratic function y = - X & # 178 / 4 be the vertex formula y = - (X-H)
RELATED INFORMATIONS
- 1. The cube with edge length a is placed in the shape shown in the figure. (1) try to find its surface area; (2) if it is placed in 10 layers, what is its surface area?
- 2. In the class of "bisector of angle", the teacher asked the students to practice a problem. The figure of the problem is shown in the figure. BD in the figure is the bisector of ABC. While the students were busy drawing and analyzing the problem, Xiaoying suddenly said excitedly: "I have a discovery!" Originally, she felt that she had created a method to draw the acute bisector in a right triangle. Her method is as follows: take a point E on AB, make be = BC, and then draw de ⊥ AB and AC at point D, then BD is the bisector of ∠ ABC? Please give reasons
- 3. After learning Chapter 2 "special triangles", the teacher assigned a question: as shown in the figure, points m and N are on the sides of BC and Ca of the regular triangle ABC, and BM = CN, am and BN intersect at point Q. (3) if the points m and N in the question are moved to the extension line of BC and Ca, and BM = CN, can we get ∠ BQM = 60 °? Please give reasons (1) Judge whether △ ABM and △ BCN are congruent and explain the reason. (2) judge whether ∠ BQM is equal to 60 ° and explain the reason
- 4. There are 35 students in class 5 (1) of Xinhua primary school. They asked the photo studio to take a group photo. Each student should take a photo, give it to the teacher and enlarge it. They should give it to each student How much is the charge? (25 yuan for group photo, 2 photos for free; 0.8 yuan for printing and 5.2 yuan for enlarging)
- 5. What things in life are related to technology
- 6. The concepts and properties of translation and axisymmetric transformation
- 7. What is the nature of rotation?
- 8. What is the definition of rotation angle
- 9. What is rolling planning method (meaning)
- 10. What is the definition of a rotating surface? It is said in the book that the surface formed by a curve rotating around a fixed line in its plane is called a rotating surface. But why does a cylinder also have a rotating surface? That surface is a rotating surface
- 11. If you translate the triangle one lattice to the left, can you show the positions of the three vertices of the triangle with pairs of numbers
- 12. After a figure is translated to a certain position, all the points on the figure are translated in the direction () and the distance of translation（
- 13. A graph is shifted from the third quadrant to the fourth quadrant. Compare the coordinates of each vertex and the position of the graph. What conclusion can you get
- 14. ① Translation by moving___ And___ The translated image is the same as the original image___ The position relation of the connecting line of the corresponding point is___ . ② Rotation by___ ,___ And___ The rotated image is the same as the original image___ . ③ Centrosymmetry is a special rotation whose degree of rotation angle is___ The line of the corresponding point is closed___ Square ④ What is the intersection point of the straight line where the corresponding points of two similar figures are located___ . ⑤ If an image is both an axisymmetric image and a centrosymmetric image, then the image can be___ .
- 15. 1. The key to determine the position of the figure after translation is translation () and () 2. The key to determine the position of the figure after rotation is rotation () and ()
- 16. Figure translation is determined by () and ()
- 17. As shown in the figure, △ ABC rotates 90 ° clockwise around point O and reaches the position of △ CDE (A) Line AB and line CD are perpendicular to each other (B) Segment AC and segment CE are perpendicular to each other (C) Segment BC and segment de are perpendicular to each other (D) Point C and point C are the corresponding points of two triangles
- 18. When the object or figure is translated, the position () size and direction (). A does not change, B changes, C cannot be determined
- 19. After a figure is enlarged or reduced, although the length of each side changes, the shape of the figure does not change
- 20. After a figure rotates, its position changes and its shape remains unchanged. Is that right?