Untuk menggambarkan sketsa grafik fungsi kuadrat
, ada 4 aspek yang perlu diperhatikan:
- Nilai
; jika
maka parabola terbuka ke atas, dan jika
maka parabola terbuka ke bawah.
- Nilai
; jika
maka parabola memotong sumbu-
di dua titik. Jika
maka parabola memotong sumbu-
, dan jika
maka parabola tidak memotong dan tidak menyinggung sumbu-
.
- Nilai
;
adalah koordinat titik potong parabola dengan sumbu-
.
- Koordinat titik ekstrim
, dengan
dan
.
Perhatikan bahwa fungsi kuadrat
mempunyai nilai
,
, dan
.
Karena
, maka parabola
terbuka ke atas.
Selanjutnya, nilai diskriminannya adalah
![begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight D equals cell b squared minus 4 a c end cell row blank equals cell open parentheses negative 4 close parentheses squared minus 4 open parentheses 1 close parentheses open parentheses 3 close parentheses end cell row blank equals cell 16 minus 12 end cell row blank equals 4 end table end style](data:image/png;base64,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)
Karena nilai
, maka parabola
memotong sumbu-
di dua titik. Koordinat titik-titik potongnya dengan sumbu-
ditentukan dengan mensubstitusikan nilai
ke fungsi kuadrat.
Perhatikan bahwa
![begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus 4 x plus 3 end cell equals 0 row cell open parentheses x minus 3 close parentheses open parentheses x minus 1 close parentheses end cell equals 0 end table end style](data:image/png;base64,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)
dan mengakibatkan
![begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell table row cell x minus 3 equals 0 end cell atau cell x minus 1 equals 0 end cell row cell x equals 3 end cell blank cell x equals 1 end cell end table end cell end table end style](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKQAAAAeCAYAAACi5LVSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAATRJrTQAAAAs1JREFUeNrtmzFIHEEUhocjiIQgiBwiKQIiQUSCEEREgk3KI11IYXWkTyWkEIsUaVKkEEkjEkJIZ2FhIVinCASxSBGEFEFEgiAhHCISOP8n72S53Hkzu/Ne5s73wY/e7s3uuP/bmTeDzzl9nkBfoXPoFNqGpgXuMwft8n32oEfOaMd9aJmfkxTJ+rEJzUAl6Bb0AvoZ+R6j0HfoIX+mn/t83PiXj1AVqgtdv6v8oKA8jnzNVeh507EqHy/KaQ8HplRAFvaDRrHZzOdBaAcaidhJGiEfQOtQpcNDuk6t+AGVm44NeY7ElFJ84anlAFq4pi8+bdoZHWK+hh++fdL245K7nOdR0PRBG9BYxA42zpF59wTeyL9tjp97tP0ETfDvlOf89jAtT5uQgJT2Q3qELOLHFS9Z76EpgU6W+K3f4JxS4wGcRRg16pHahJov7cf/CMggP0b5QvPCeUuZE9yYU8R+iymizFNHJ2jE/gD94b/fJ7jytAk1X8MPqSm7iB9XX/4MPYNeCQckjZQ1gSS62iKJfufR9hu0CN0OGO1C24wHBqSWH5KLmrx+uDucME/y5zUXd59wKzNFD0BvoBWhbYbG1DbDb6PPNkONF1slXmyRScOZ87Qj8DiwzRGnJ3T+KQewr/nSfmgEZG4/+jhg5ppWQ7SC7I/UuQon6DT9HEKveesnNrS42OPEedf5b8TSCvmEtQS9hX5lzk/wM6oHtKnwipL6ss0LEh/zNfxwORY/mn4YhmEYhmEYhmEYhmEYhmEYhmEYRgG06nYMfzTqdpJFo27HCEO6bqerkKjbMfKRXECG1ocU+Zd837qdm4ymH0kGZEh9SNE3UbJup1fQ8iPZgCQ06kMaI6RU3U4voeVHsgEZUh9SdIogOtXt3HQ0/UguIDXrdbIjZc3iLgk/kgpIrfoQjbqdXkCzXie5gNSqD3FOr26nm9H0w/lO7xdHXTYyMetorQAAAhh0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIiB4bWxuczp3cnM9Imh0dHA6Ly93d3cud2lyaXMuY29tL3htbC9tYXRobWwtZXh0ZW5zaW9uIj48bXRhYmxlIGNvbHVtbmFsaWduPSJyaWdodCBjZW50ZXIgbGVmdCIgY29sdW1uc3BhY2luZz0iMHB4Ij48bXRyPjxtdGQvPjxtdGQvPjxtdGQ+PG10YWJsZSB3cnM6Y29sdW1uYWxpZ249InJlbGF0aW9uIGNlbnRlciByZWxhdGlvbiI+PG10cj48bXRkPjxtaT54PC9taT48bW8+LTwvbW8+PG1uPjM8L21uPjxtbz49PC9tbz48bW4+MDwvbW4+PC9tdGQ+PG10ZD48bWk+YXRhdTwvbWk+PC9tdGQ+PG10ZD48bWk+eDwvbWk+PG1vPi08L21vPjxtbj4xPC9tbj48bW8+PTwvbW8+PG1uPjA8L21uPjwvbXRkPjwvbXRyPjxtdHI+PG10ZD48bWk+eDwvbWk+PG1vPj08L21vPjxtbj4zPC9tbj48L210ZD48bXRkLz48bXRkPjxtaT54PC9taT48bW8+PTwvbW8+PG1uPjE8L21uPjwvbXRkPjwvbXRyPjwvbXRhYmxlPjwvbXRkPjwvbXRyPjwvbXRhYmxlPjwvbWF0aD4Fz2TIAAAAAElFTkSuQmCC)
sehingga koordinat titik- titik potong parabola dengan sumbu-
adalah
dan
.
Berikutnya, karena
maka koordinat titik potong parabola dengan sumbu-
adalah
.
Terakhir, kita akan menghitung koordinat titik puncak parabola
.
![begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript p end cell equals cell negative fraction numerator b over denominator 2 a end fraction end cell row blank equals cell negative fraction numerator open parentheses negative 4 close parentheses over denominator 2 left parenthesis 1 right parenthesis end fraction end cell row blank equals 2 end table end style](data:image/png;base64,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)
dan
Jadi, koordinat titik puncak grafik fungsi kuadrat
adalah
.
Dengan demikian, sketsa grafik fungsi kuadrat
adalah
![](https://imgix2.ruangguru.com/assets/miscellaneous/png_bfimne_3755.PNG)