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As shown in the figure, if the parabola Y1 = - x2 + 2 is shifted one unit to the right to get the parabola Y2, then the area of the shadow part in the figure is () A. 2B. 3C. 4D
As shown in the figure below, ∵ parabola Y1 = - x2 + 2 shifts 1 unit to the right to get parabola Y2, ∵ the lines of the two vertices are parallel to the X axis, ∵ the shadow part in the graph and the red part in the graph are equal to the area of the red part, ∵ the shadow part in the graph is equal to the area of the red part, and the red part is a rectangle with the length and width of 2, 1 respectively, ∵ the area of the shadow part in the graph is s = 2
RELATED INFORMATIONS
- 1. The parabola Y1 = 2x2 is translated to the right by 2 units to obtain the image of parabola Y2 as shown in the figure. P is a moving point on the symmetry axis of parabola Y2. The line x = t is parallel to the Y axis, and intersects with the line y = x and parabola Y2 at points a and B respectively. If △ ABP is an isosceles right angled triangle with point a or point B as the right angle vertex, then t is the value of T satisfying the condition=______ ．
- 2. (1) translate the parabola Y1 = 2x2 two units to the right to get the parabola Y2 Ask 2010 Zhejiang Yiwu high school entrance examination question 16 very detailed analysis? 16. (1) translate the parabola Y1 = 2x2 two units to the right, and get the result For the image of parabola Y2, then y2 = ■; (2) As shown in the figure, P is a moving point on the symmetry axis of the parabola Y2, The straight line x = t is parallel to the Y axis, and is respectively parallel to the straight line y = x The parabola Y2 intersects at points a and B. If △ ABP is a parabola Or an isosceles right triangle whose point B is a right vertex If the value of T is sufficient, then t = 0 can be found in the graph. Don't copy the analytic answers they wrote for me
- 3. It is known that the parabola y ^ 2 = 2x (P greater than 0), passing through point (1,0) as a straight line with slope k, intersects parabola at two points a and B. the symmetric point of point a about X axis is C It is known that the parabola y ^ 2 = 2x (P is greater than 0), passing through point (1,0) as a straight line with slope k, l intersects the parabola at two points a and B, the symmetric point of point a about X axis is C, and the straight line BC intersects X axis at Q. try to prove that when k changes, q is a fixed point
- 4. It is known that the parabolic equation y ^ 2 = 4x, the straight line L passes through the fixed point P (- 2,1), and the slope is K. when k is the value, the straight line L and the parabola have two common points
- 5. It is known that the equation of parabola is y quadratic = 4x, the straight line I passes through the fixed point P (- 2.1), and the slope is K It is known that the equation of parabola is y quadratic = 4x, the straight line I passes through the fixed point P (- 2.1), and the slope is K. when the value of K is, the straight line and parabola have only one common point and two common points
- 6. It is known that the parabolic equation y = 4x square, the straight line L passes P (- 2,1), and the slope is K. when what is the value of K, there is only one common point between the straight line L and the parabola There are two common points, no common points? Ask for detailed explanation
- 7. Given that Y1 = 2x-1, y2 = 5x + 7, when x is what value, Y1 is smaller than Y2 by 1
- 8. Let Y1 = 1 / 5x + 1, y2 = (2x + 1) / 4, when what is the value of X, Y1 and Y2 are opposite numbers to each other? (solved by a linear equation of one variable)
- 9. Let Y1 = 1 / 5x + 1, y2 = 2x + 1 / 4, when what is the value of X, Y1 and Y2 are opposite numbers?
- 10. Given that Y1 = 2x + 1, y2 = 5x-8, when what is the value of X, are Y1 and Y2 opposite to each other?
- 11. It is known that two points a (1, Y1), B (2, Y2) on the parabola y = - x ^ 2 + 2x + 1 compare the sizes of Y1 and Y2. (try to solve it in many ways)
- 12. Given the parabola Y1 = ax Λ 2-2x + C through (0, - 1) inverse scale function y2 = K / X through (1, a), compare the size of Y1 and Y2
- 13. Given that a (- 2, Y1), B (- 1, Y2) and C (2, Y3) are all on the square of the parabola y = 2x, then the size relation of Y1, Y2 and Y3 is
- 14. It is known that the opening direction and size of the parabola Y1 = a (X-H) &# 178; + K and y2 = (X-2) &# 178; - 7 are the same, and the lowest point is the same It is known that the opening direction and size of the parabola Y1 = a (X-H) & # 178; + K and y2 = (X-2) & # 178; - 7 are the same, and the coordinates of the lowest point are (- 1, - 2). Find the functional relationship of the parabola Y1, and point out whether the parabola Y1 can be obtained by Y2 translation, and if so, how to translate it
- 15. It is known that Y1 = 4x + 8, y2 = 3x-7 When x takes what value, Y1 and Y2 are opposite to each other
- 16. 1. Given that Y1 = - x 3, y2 = 3x-4, when x takes what value, Y1 > Y2? How do you do it?
- 17. It is known that Y1 = 3x-2, y2 = 4x-7 (1) When x goes to what value, the values of Y1 and Y2 are equal? (2) when x goes to what value, Y1 is less than Y2 by 6? (3) when x takes what value, Y1 and Y2 are opposite to each other?
- 18. Is the following shift correct? Wrong correction. From 2x = X-5 to 2x-x = 5; from 4x + 1 = 2x + 3 to 4x + 2x = 1 + 3; from 2x-1 = 3x + 3 to 2x-3x = 3 + 1
- 19. It is known that: Y1 = 2 (3x + 4), y2 = 5 (2x-8) when x takes what value, (1) Y1 and Y2 are opposite to each other? (2) y 2 smaller than Y2?
- 20. Given that Y1 = 2 (3x + 4), y2 = 5 (2x-7), when x is what value, Y1 is 3 times larger than Y2