{
"query": {
"display": "intersecciones $$f\\left(x\\right)=\\left(x-4\\right)^{2}$$",
"symbolab_question": "CONIC#intercepts f(x)=(x-4)^{2}"
},
"solution": {
"level": "PERFORMED",
"subject": "Functions & Graphing",
"topic": "Functions",
"subTopic": "intercepts",
"default": "\\mathrm{X\\:intersecta}: (4,0),\\mathrm{Y\\:intersecta}: (0,16)",
"meta": {
"showVerify": true
}
},
"steps": {
"type": "interim",
"title": "Puntos de intersección con el eje de $$\\left(x-4\\right)^{2}:\\quad\\:$$X intersecta$$:\\:\\left(4,\\:0\\right),\\:$$Y intersecta$$:\\:\\left(0,\\:16\\right)$$",
"steps": [
{
"type": "interim",
"title": "Puntos de intersección con el eje de las abscisas (x) de $$\\left(x-4\\right)^{2}:{\\quad}\\left(4,\\:0\\right)$$",
"input": "\\left(x-4\\right)^{2}",
"steps": [
{
"type": "definition",
"title": "Definición de puntos de intersección con el eje de las abscisas (x)",
"text": "La intersección con el eje de las abscisas (x), es un punto de la grafica donde $$y=0$$"
},
{
"type": "interim",
"title": "Resolver $$\\left(x-4\\right)^{2}=0:{\\quad}x=4$$",
"input": "\\left(x-4\\right)^{2}=0",
"steps": [
{
"type": "step",
"primary": "Usando la propiedad del factor cero:$$\\quad$$ Si $$ab=0\\:$$entonces $$a=0\\:$$o $$b=0$$"
},
{
"type": "interim",
"title": "Resolver $$x-4=0:{\\quad}x=4$$",
"input": "x-4=0",
"steps": [
{
"type": "interim",
"title": "Desplace $$4\\:$$a la derecha",
"input": "x-4=0",
"result": "x=4",
"steps": [
{
"type": "step",
"primary": "Sumar $$4$$ a ambos lados",
"result": "x-4+4=0+4"
},
{
"type": "step",
"primary": "Simplificar",
"result": "x=4"
}
],
"meta": {
"interimType": "Move to the Right Title 1Eq",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7aG2xrz8nLi1pnXB+ypYxF5N1pXT08zEQpn0WJ6CFMXDCwtftDeQ8GSpiqhtwMwQBPlRMTLc8dpF+T7mmaRQSVuqEVSMHyl6Fi8wmVlQohhGsHuCWujTcybm8y4lstc3AiiuTvHZMNMidREaJCrkWGZ37QFwBVrUvPiUXbYPoTV+1RybsQo6Jq4S5YcdCCt1sC4urHZT54SE8mq2mCeDxrTJj90rawuxqAJRl9Ya/3QO+6Hk6xbVc4+zMe7qHNsLwY+4Y6zQSLc4TQkYdmdqOYPpmRyRpQMVLh8QfMrDSF0WmxHtSc2ig2CQSJwrhOZ803WA9L/4M2+x5MgHkI4V3ibWOsnPai4TwkGNIoFgxxGKlOWMQy81uHSddR9VXK3ZDtJYkJTEU8yVJgCG778QCuW4Cb/ZbTphLLCAUVg9XKanfHQ9C6OgiFDRGAqrbHwB4Jv1NSh0LFaB8tpxaRUg6QY41UqQWZGj34KS5miiboj98fqRW9q74Q1HtrCEBT6YS+VcVCInWTKMQboQYcz4khgWuN9Yh6bBkR0JYX1YgkpQByDZ/Qigkd8VglsnpK4Td"
}
}
],
"meta": {
"solvingClass": "Equations",
"interimType": "Generic Solve Title 1Eq"
}
},
{
"type": "step",
"primary": "La solución a la ecuación de segundo grado es:",
"result": "x=4"
}
],
"meta": {
"solvingClass": "Equations",
"interimType": "Generic Solve Title 1Eq"
}
},
{
"type": "step",
"result": "\\left(4,\\:0\\right)"
}
],
"meta": {
"solvingClass": "Function Intersect",
"interimType": "Interception X Points Top 1Eq",
"gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMi0yMe2UGvILAl+uMDY3PBvpmRyRpQMVLh8QfMrDSF0VM+2OIL0qxu5HS8fSWt6I0WliQcf9vaFvjiH70iMSCK+H0xHQIKG005c/V+EDYRRGRQaZXqscfwTf2BFuSlLFItUcm7EKOiauEuWHHQgrdbAuLqx2U+eEhPJqtpgng8a0yY/dK2sLsagCUZfWGv90DWuhuNXgfM/X3cHm7npbgtI8BPOx0wlsgFN8qUa6AzA0="
}
},
{
"type": "interim",
"title": "Puntos de intersección con el eje de las ordenadas (y) de $$\\left(x-4\\right)^{2}:{\\quad}\\left(0,\\:16\\right)$$",
"input": "\\left(x-4\\right)^{2}",
"steps": [
{
"type": "definition",
"title": "Definición de puntos de intersección con el eje de las ordenadas (y)",
"text": "La intersección con el eje de las ordenadas (y), es un punto de la grafica donde $$x=0$$"
},
{
"type": "interim",
"title": "Resolver $$y=\\left(0-4\\right)^{2}:{\\quad}y=16$$",
"input": "y=\\left(0-4\\right)^{2}",
"steps": [
{
"type": "interim",
"title": "Simplificar $$\\left(0-4\\right)^{2}:{\\quad}16$$",
"input": "\\left(0-4\\right)^{2}",
"steps": [
{
"type": "step",
"primary": "Restar: $$0-4=-4$$",
"result": "=\\left(-4\\right)^{2}"
},
{
"type": "step",
"primary": "Aplicar las leyes de los exponentes: $$\\left(-a\\right)^{n}=a^{n},\\:$$si $$n$$ es par",
"secondary": [
"$$\\left(-4\\right)^{2}=4^{2}$$"
],
"result": "=4^{2}"
},
{
"type": "step",
"primary": "$$4^{2}=16$$",
"result": "=16"
}
],
"meta": {
"solvingClass": "Solver",
"interimType": "Generic Simplify Specific 1Eq",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7rsLKCW/yKKFM+tShRnQiVN13jtrSFDx+UNsawjlOjV1pDjGlV0QXxhP2pBsH2aZo8LfSxJ+0AgVLpCSnLX0iSqxTv8YLp5eCfB23VU7pNlRuB65a4g/UHBJEv+IIm4i7"
}
},
{
"type": "step",
"result": "y=16"
}
],
"meta": {
"solvingClass": "Equations",
"interimType": "Generic Solve Title 1Eq"
}
},
{
"type": "step",
"result": "\\left(0,\\:16\\right)"
}
],
"meta": {
"solvingClass": "Function Intersect",
"interimType": "Interception Y Points Top 1Eq",
"gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMi0yMe2UGvILAl+uMDY3PBvpmRyRpQMVLh8QfMrDSF0WmxHtSc2ig2CQSJwrhOZ803WA9L/4M2+x5MgHkI4V3iRKdp4ME03ZJIAvib3dKmCJkREHZzeifGHefy9VJIB8VHM2VKpXH/YUXme0pCsADcH9OwzYCvqTUjsRdf0lKZz3RKIgK8XGPIhsV1nCpqQ3ZtQt9r0/0c4bvg6Gc3fSf2cXcN6cRaiMtIZdgwNwCXts="
}
},
{
"type": "step",
"result": "\\mathrm{X\\:intersecta}:\\:\\left(4,\\:0\\right),\\:\\mathrm{Y\\:intersecta}:\\:\\left(0,\\:16\\right)"
}
],
"meta": {
"solvingClass": "Function Intersect"
}
},
"plot_output": {
"meta": {
"plotInfo": {
"variable": "x",
"plotRequest": "(x-4)^{2}"
},
"showViewLarger": true
}
},
"meta": {
"showVerify": true
}
}
Solución
intersecciones
Solución
Pasos de solución
Puntos de intersección con el eje de las abscisas (x) de
Puntos de intersección con el eje de las ordenadas (y) de