1 xác định hàm số a,c của hàm số y= ax^2 +x +c b) parabol đi qua 1 điểm (3, -4) có trục đối xứng= -3 phần 2 c) parabol có đỉnh i( 2,-2) d) parapol đi qua điểm d( -1,6) có tung độ = -1 phần 4

\[\begin{array}{l} y = a{x^2} + x + c\,\,\,\,\left( P \right)\\ b)\,\,\,\left( P \right)\,\,\,co\,\,\,truc\,\,doi\,\,xung\,\,la\,\,\,x = - \frac{3}{2}\\ \Rightarrow - \frac{1}{{2a}} = - \frac{3}{2} \Leftrightarrow a = \frac{1}{3} \Rightarrow \left( P \right):\,\,\,y = \frac{1}{3}{x^2} + x + c.\\ \left( P \right)\,\,\,di\,\,\,qua\,\,diem\,\,\,\left( {3; - 4} \right)\\ \Rightarrow - 4 = \frac{1}{3}{.3^2} + 3 + c \Leftrightarrow c = - 10.\\ Vay\,\,\,a = \frac{1}{3};\,\,c = - 10.\\ c)\,\,\,I\left( {2;\,\, - 2} \right)\\ \left( P \right)\,\,\,co\,\,\,dinh\,\,\,I\left( {2;\,\, - 2} \right)\\ \Rightarrow \left\{ \begin{array}{l} - \frac{1}{{2a}} = 2\\ a{.2^2} + 2 + c = - 2 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} a = - \frac{1}{4}\\ c = - 5 \end{array} \right.\\ Vay\,\,\,a = - \frac{1}{4};\,\,\,c = - 5.\\ d)\,\,\,\left( P \right)\,\,\,\,cat\,\,\,Oy\,\,\,tai\,\,\,diem\,\,\,co\,\,tung\,\,do\,\,\, = - \frac{1}{4}\\ \Rightarrow \left( P \right)\,\,\,\,di\,\,\,qua\,\,\,C\left( {0; - \frac{1}{4}} \right)\\ \Rightarrow c = - \frac{1}{4}.\\ \Rightarrow \left( P \right):\,\,\,y = a{x^2} + x - \frac{1}{4}\\ \left( P \right)\,\,\,\,di\,\,\,qua\,\,\,\,D\left( { - 1;\,\,6} \right)\\ \Rightarrow 6 = a.1 - 1 - \frac{1}{4}\\ \Rightarrow a = \frac{{29}}{4}.\\ Vay\,\,\,\,a = \frac{{29}}{4},\,\,\,c = - \frac{1}{4}. \end{array}\]