intercepts of f(x)=3x^2+3y^2+30y=0

{ "query": { "display": "intercepts $$f\\left(x\\right)=3x^{2}+3y^{2}+30y=0$$", "symbolab_question": "FUNCTION#intercepts f(x)=3x^{2}+3y^{2}+30y=0" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Functions", "subTopic": "intercepts", "default": "\\mathrm{Y\\:Intercepts}: (0,0)", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Axis interception points of $$0:\\quad\\:$$Y Intercepts$$:\\:\\left(0,\\:0\\right)$$", "steps": [ { "type": "interim", "title": "$$x-$$axis interception points of $$0:{\\quad}$$None", "input": "0", "steps": [ { "type": "definition", "title": "x-axis interception points definition", "text": "x-intercept is a point on the graph where $$y=0$$" }, { "type": "interim", "title": "Solve $$0=0:{\\quad}$$True", "input": "0=0", "steps": [ { "type": "step", "primary": "Both sides are equal", "result": "\\mathrm{True}" } ], "meta": { "solvingClass": "Equations", "interimType": "Generic Solve Title 1Eq" } }, { "type": "step", "result": "\\mathrm{No\\:x-axis\\:interception\\:points}" } ], "meta": { "solvingClass": "Function Intersect", "interimType": "Interception X Points Top 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMXsqdoP/+t8mkG9iMyF4x8bt5g+KB4e7b6i2FR+k9P7PhrOw/87AhYlSIaBiZ+9c8DX0k+EM/0vwN/YfwBX0du5KbKNRP2lUnpKreVmLXLgw1m5xab0OAea1uypKEYFnD" } }, { "type": "interim", "title": "$$y-$$axis interception point of $$0:{\\quad}\\left(0,\\:0\\right)$$", "input": "0", "steps": [ { "type": "definition", "title": "y-axis interception points definition", "text": "$$y$$-intercept is the point on the graph where $$x=0$$" }, { "type": "step", "result": "y=0" }, { "type": "step", "result": "\\left(0,\\:0\\right)" } ], "meta": { "solvingClass": "Function Intersect", "interimType": "Interception Y Points Top 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMoY5LPa3x5862ED2Fb21Kz+w/rOyd5aPv89U4pRBmcfn/5utQUvpyWuzqGdNN8sTzDm0ZOvA+Ygb668PxLRGXFzczxXhjhAZFo7dyFFV2xFTcXxDiV57AORvmJmjFBhGj" } }, { "type": "step", "result": "\\mathrm{Y\\:Intercepts}:\\:\\left(0,\\:0\\right)" } ], "meta": { "solvingClass": "Function Intersect" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "0" }, "showViewLarger": true } }, "meta": { "showVerify": true } }