a.Xác định parabol (p): y=ax2+bx+1, biết đỉnh của nó là I(2;-3)
b.Lập bảng biến thiên và vẽ đồ thị của (p) ở câu a
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Parabol y = ax2 + bx + 2 có đỉnh I(2 ; –2), suy ra :
Từ (1) ⇒ b2 = 16.a2, thay vào (2) ta được 16a2 = 16a ⇒ a = 1 ⇒ b = –4.
Vậy parabol cần tìm là y = x2 – 4x + 2.
+ Parabol y = ax2 + bx + 2 đi qua điểm B(–1 ; 6)
⇒ 6 = a.( –1)2 + b.( –1) + 2 ⇒ a = b + 4 (1)
+ Parabol y = ax2 + bx + 2 có tung độ của đỉnh là –1/4
Thay (1) vào (2) ta được: b2 = 9.(b + 4) ⇔ b2 – 9b – 36 = 0.
Phương trình có hai nghiệm b = 12 hoặc b = –3.
Với b = 12 thì a = 16.
Với b = –3 thì a = 1.
Vậy có hai parabol thỏa mãn là y = 16x2 + 12b + 2 và y = x2 – 3x + 2.
+ Parabol y = ax2 + bx + c đi qua điểm A (8; 0)
⇒ 0 = a.82 + b.8 + c ⇒ 64a + 8b + c = 0 (1).
+ Parabol y = ax2 + bx + c có đỉnh là I (6 ; –12) suy ra:
–b/2a = 6 ⇒ b = –12a (2).
–Δ/4a = –12 ⇒ Δ = 48a ⇒ b2 – 4ac = 48a (3) .
Thay (2) vào (1) ta có: 64a – 96a + c = 0 ⇒ c = 32a.
Thay b = –12a và c = 32a vào (3) ta được:
(–12a)2 – 4a.32a = 48a
⇒ 144a2 – 128a2 = 48a
⇒ 16a2 = 48a
⇒ a = 3 (vì a ≠ 0).
Từ a = 3 ⇒ b = –36 và c = 96.
Vậy a = 3; b = –36 và c = 96.
(P) : y = ax2 + bx + c
Parabol có đỉnh I(1 ; 4) ⇒ –b/2a = 1 ⇒ b = –2a ⇒ 2a + b = 0.
Parabol đi qua I(1; 4) ⇒ 4 = a.12 + b . 1 + c ⇒ a + b + c = 4.
Paraol đi qua D(3; 0) ⇒ 0 = a.32 + b.3 + c ⇒ 9a + 3b + c = 0.
Giải hệ phương trình
ta được : a = –1 ; b = 2 ; c = 3.
Vậy a = –1 ; b = 2 ; c = 3.
Sửa đề: cắt trục tung tại điểm có tung độ bằng -3
Thay x=0 và y=-3 vào (P), ta được:
\(a\cdot0^2+b\cdot0+c=-3\)
=>0+0+c=-3
=>c=-3
vậy: (P): \(y=ax^2+bx-3\)
Tọa độ đỉnh là I(-1;-4) nên ta có:
\(\left\{{}\begin{matrix}-\dfrac{b}{2a}=-1\\-\dfrac{b^2-4\cdot a\cdot\left(-3\right)}{4a}=-4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}b=2a\\\dfrac{b^2+12a}{4a}=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}b=2a\\\left(2a\right)^2+12a=16a\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}b=2a\\4a^2-4a=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}b=2a\\4a\left(a-1\right)=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}b=2a\\\left[{}\begin{matrix}a=0\left(loại\right)\\a-1=0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=1\\b=2\end{matrix}\right.\)
Lời giải:
Theo bài ra thì tọa độ đỉnh của parabol là $(-2,19)$
Từ hàm $y=ax^2+bx+3=a(x+\frac{b}{2a})^2+3-\frac{b^2}{4a}$ ta có tọa độ đỉnh của parabol là:
$(\frac{-b}{2a}, 3-\frac{b^2}{4a})$
$\Rightarrow \frac{-b}{2a}=-2; 3-\frac{b^2}{4a}=19$
$\Rightarrow a=-4; b=-16$
Parabol y = ax2 + bx + c có:
+ Tọa độ đỉnh D là:
+ Phương trình trục đối xứng là:
a, Có đỉnh \(I\left(-\dfrac{b}{2a};-\dfrac{\Delta}{4a}\right)\)
\(\Rightarrow\left\{{}\begin{matrix}-\dfrac{b}{2a}=2\\4a+2b+1=-3\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}4a+b=0\\4a+2b=-4\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}a=1\\b=-4\end{matrix}\right.\)
Vậy parabol đó có dạng là \(\left(P\right):y=x^2-4x+1\).
b,![](data:image/png;base64,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)