Bilamizki, \(f\left( y \right) = a{y^2} + by + c\) ning grafigi, agar \(a > 0\) bo‘lsa, o‘ngga, \(a < 0\) bo‘lsa, chapga ochiladigan parabola bo‘ladi. Biz uning cho'qqisini ham bilamiz,

\[\left( {f\left( { - \frac{b}{{2a}}} \right), - \frac{b}{{2a}}} \right)\]

Parabolaning \(x\)-kesishmasi \(\left( {f\left( 0 \right),0} \right) = \left( {c,0} \right)\) nuqtasi va \(y\)-kesishmalar (agar mavjud bo'lsa) \(f\left( y \right) = 0\) ni yechish orqali topiladi.

Shunday qilib, yoki bizning holatimizda biz chap tomonga ochiladigan va uning cho'qqisida joylashgan parabola borligini bilamiz,

\[\left( {f\left( { - \frac{8}{{2\left( { - 4} \right)}}} \right), - \frac{8}{{2\left( { - 4} \right)}}} \right) = \left( {f\left( 1 \right),1} \right) = \left( {7,1} \right)\]

Bundan tashqari, \(x\)-kesishmasi \(\left( {3,0} \right)\) ekanligini ko'rishimiz mumkin.

\(y\)-kesishmalarini topish uchun biz qilishimiz kerak bo'lgan yagona narsa: \( - 4{y^2} + 8y + 3 = 0\).

\[y = \frac{{ - 8 \pm \sqrt {{8^2} - 4\left( { - 4} \right)\left( 3 \right)} }}{{2\left( { - 4} \right)}} = \frac{{ - 8 \pm \sqrt {112} }}{{ - 8}} = \frac{{ - 8 \pm 4\sqrt 7 }}{{ - 8}} = \frac{{2 \pm \sqrt 7 }}{2} = - 0.3229,\,\,\,2.3229\]

Shunday qilib, ikkita \(y\)-kesishmalar: \(\left( {0, - 0.3229} \right)\) va \(\left( {0,2.3229} \right)\).

Mana bu parabolaning eskizi.