A Cubic Read from Its Graph
Difficulty: Medium · Topics: Algebra, Polynomials, Polynomial Equations
Grafikdan o‘qilgan kub ko‘phad
The graph of the cubic y=P(x) crosses the x-axis at -2, 1 and 3, and the y-axis at 3.
graph "x":[-3,4.6],"y":[-4.5,5.2],"xTicks":[],"yTicks":[],"clip":true,"label":"Cubic graph crossing the x-axis at -2, 1 and 3 and the y-axis at 3","items":["type":"curve","points":[[-2.45,-4.231],[-2.382,-3.479],[-2.314,-2.769],[-2.247,-2.101],[-2.179,-1.473],[-2.111,-0.883],[-2.043,-0.333],[-1.976,0.181],[-1.908,0.658],[-1.84,1.1],[-1.772,1.507],[-1.704,1.88],[-1.637,2.221],[-1.569,2.53],[-1.501,2.808],[-1.433,3.057],[-1.366,3.276],[-1.298,3.467],[-1.23,3.632],[-1.162,3.77],[-1.094,3.883],[-1.027,3.972],[-0.959,4.037],[-0.891,4.08],[-0.823,4.101],[-0.756,4.102],[-0.688,4.084],[-0.62,4.046],[-0.552,3.991],[-0.484,3.92],[-0.417,3.832],[-0.349,3.729],[-0.281,3.613],[-0.213,3.483],[-0.146,3.341],[-0.078,3.188],[-0.01,3.025],[0.058,2.852],[0.126,2.671],[0.193,2.483],[0.261,2.288],[0.329,2.087],[0.397,1.882],[0.464,1.673],[0.532,1.462],[0.6,1.248],[0.668,1.034],[0.736,0.819],[0.803,0.606],[0.871,0.394],[0.939,0.185],[1.007,-0.02],[1.074,-0.22],[1.142,-0.415],[1.21,-0.603],[1.278,-0.784],[1.346,-0.956],[1.413,-1.119],[1.481,-1.272],[1.549,-1.413],[1.617,-1.543],[1.684,-1.659],[1.752,-1.761],[1.82,-1.848],[1.888,-1.919],[1.956,-1.974],[2.023,-2.011],[2.091,-2.029],[2.159,-2.027],[2.227,-2.005],[2.294,-1.961],[2.362,-1.895],[2.43,-1.805],[2.498,-1.692],[2.566,-1.553],[2.633,-1.387],[2.701,-1.195],[2.769,-0.975],[2.837,-0.725],[2.904,-0.446],[2.972,-0.136],[3.04,0.206],[3.108,0.58],[3.176,0.988],[3.243,1.431],[3.311,1.909],[3.379,2.424],[3.447,2.976],[3.514,3.567],[3.582,4.196],[3.65,4.866]],"start":"arrow","end":"arrow","type":"point","at":[-2,0],"label":"−2","anchor":"nw","italic":false,"type":"point","at":[1,0],"label":"1","anchor":"ne","italic":false,"type":"point","at":[3,0],"label":"3","anchor":"se","italic":false,"type":"point","at":[0,3],"label":"3","anchor":"ne","italic":false,"type":"label","at":[3.3,4.6],"text":"y = P(x)","anchor":"w","size":13]
Find P(4).
y=P(x) kub ko‘phadning grafigi x o‘qini -2, 1 va 3 da, y o‘qini esa 3 da kesib o‘tadi.
graph "x":[-3,4.6],"y":[-4.5,5.2],"xTicks":[],"yTicks":[],"clip":true,"label":"Cubic graph crossing the x-axis at -2, 1 and 3 and the y-axis at 3","items":["type":"curve","points":[[-2.45,-4.231],[-2.382,-3.479],[-2.314,-2.769],[-2.247,-2.101],[-2.179,-1.473],[-2.111,-0.883],[-2.043,-0.333],[-1.976,0.181],[-1.908,0.658],[-1.84,1.1],[-1.772,1.507],[-1.704,1.88],[-1.637,2.221],[-1.569,2.53],[-1.501,2.808],[-1.433,3.057],[-1.366,3.276],[-1.298,3.467],[-1.23,3.632],[-1.162,3.77],[-1.094,3.883],[-1.027,3.972],[-0.959,4.037],[-0.891,4.08],[-0.823,4.101],[-0.756,4.102],[-0.688,4.084],[-0.62,4.046],[-0.552,3.991],[-0.484,3.92],[-0.417,3.832],[-0.349,3.729],[-0.281,3.613],[-0.213,3.483],[-0.146,3.341],[-0.078,3.188],[-0.01,3.025],[0.058,2.852],[0.126,2.671],[0.193,2.483],[0.261,2.288],[0.329,2.087],[0.397,1.882],[0.464,1.673],[0.532,1.462],[0.6,1.248],[0.668,1.034],[0.736,0.819],[0.803,0.606],[0.871,0.394],[0.939,0.185],[1.007,-0.02],[1.074,-0.22],[1.142,-0.415],[1.21,-0.603],[1.278,-0.784],[1.346,-0.956],[1.413,-1.119],[1.481,-1.272],[1.549,-1.413],[1.617,-1.543],[1.684,-1.659],[1.752,-1.761],[1.82,-1.848],[1.888,-1.919],[1.956,-1.974],[2.023,-2.011],[2.091,-2.029],[2.159,-2.027],[2.227,-2.005],[2.294,-1.961],[2.362,-1.895],[2.43,-1.805],[2.498,-1.692],[2.566,-1.553],[2.633,-1.387],[2.701,-1.195],[2.769,-0.975],[2.837,-0.725],[2.904,-0.446],[2.972,-0.136],[3.04,0.206],[3.108,0.58],[3.176,0.988],[3.243,1.431],[3.311,1.909],[3.379,2.424],[3.447,2.976],[3.514,3.567],[3.582,4.196],[3.65,4.866]],"start":"arrow","end":"arrow","type":"point","at":[-2,0],"label":"−2","anchor":"nw","italic":false,"type":"point","at":[1,0],"label":"1","anchor":"ne","italic":false,"type":"point","at":[3,0],"label":"3","anchor":"se","italic":false,"type":"point","at":[0,3],"label":"3","anchor":"ne","italic":false,"type":"label","at":[3.3,4.6],"text":"y = P(x)","anchor":"w","size":13]
P(4) ni toping.