Math topic中文

Sketching quadratic

sketching the graphs of quadratic functions given in the form:

  • y=(x−p)2+qy = (x - p)^{2} + q
  • y=−(x−p)2+qy = -(x - p)^{2} + q
  • y=(x−a)(x−b)y = (x - a)(x - b)
  • y=−(x−a)(x−b)y = -(x - a)(x - b)

Practice questions

  1. 1Sketch the graph of y=16−(x+3)2y = 16 - (x + 3)^2 on the axes below, indicating clearly the coordinates of the intercepts and the…
  2. 2Express −x2+4x+12-x^2+4x+12 in the form −(x+p)(x−q)-(x+p)(x-q). Answer ... Sketch the graph of y=−x2+4x+12y=-x^2+4x+12 on the axes below. Indicat…
  3. 3Part of the graph of a quadratic function is shown below. The graph passes through the point A (1, 15) and it cuts the x…
  4. 4By expressing x2−10x−2x^2-10x-2 in the form (x−h)2+k(x-h)^2+k, where hh and kk are constants, write down the coordinates of the mi…
  5. 5Sketch the graph of y=−(x−2)2+4y=-(x-2)^2+4 on the axes below. Indicate clearly the coordinates of the points where the graph cro…
  6. 6Complete the table of values for y=x2+2x−1y = x^2 + 2x - 1 On the grid opposite, draw the graph of y=x2+2x−1y = x^2 + 2x - 1 for −4≤x≤2-4 \le x \le 2…
  7. 7Express x2−4x+8x^2-4x+8 in the form (x+p)2+q(x+p)^2+q. Answer ... Hence explain why there is no solution for x2−4x+8=0x^2-4x+8=0. Answer .…
  8. 8Express x2−6x+18x^{2} - 6x + 18 in the form (x−p)2+q(x - p)^{2} + q. Hence, sketch the graph of y=x2−6x+18y = x^{2} - 6x + 18 on the axes be…
  9. 9x2−4x+5=(x−a)2+bx^2 - 4x + 5 = (x - a)^2 + b Find the value of aa and of bb. Answer a = ... b = ... The curve y=x2−4x+5y = x^2 - 4x + 5 is…
  10. 10Express 1+x2−5x1+x^2-5x in the form of (x+a)2+b(x+a)^2+b. Answer ... Write down the equation of line of symmetry of the graph of y=1+x2−5xy=1+x^2-5x…
  11. 11Leanne says that the equation of the line AB is 2y=−4x+12y = -4x + 1 and the equation of the line PQ is 4y=−9x+24y = -9x + 2. Is she…
  12. 12Express x2+5x+4x^2 + 5x + 4 in the form (x+p)2+q(x + p)^2 + q. Answer (a) ... Sketch the graph of y=x2+5x+4y = x^2 + 5x + 4. Indicate clea…
  13. 13Show that y=5−x2−4xy = 5 - x^2 - 4x has a maximum point (−2,9)(-2, 9). Answer Sketch the graph of y=5−x2−4xy = 5 - x^2 - 4x on the axes be…
  14. 14Sketch the graph of y=5−(x−2)2y = 5 - (x - 2)^2, showing clearly the turning point and the y-intercept. Using your graph, explai…
  15. 15Sketch the graph of y=(2+x)(x−6)y=(2+x)(x-6) on the axes below. Indicate clearly the values where the graph crosses the axes and w…
  16. 16Sketch the graph of y=(x+4)(10−x)y=(x+4)(10-x) on the axes below. Indicate clearly the coordinates of the points where the graph cr…
  17. 17Sketch the graph of y=(3−x)(x+2)y=(3-x)(x+2) on the axes below. Indicate clearly the coordinates of the points where the graph cro…
  18. 18Express y=−(x+2)(x−5)y = -(x + 2)(x - 5) in the form of y=−(x+p)2+ky = -(x + p)^2 + k. State the value of pp and the value of kk. Answer:…