Answer:
y = -1/4x^2 - x + 3
Step-by-step explanation:
(-6,0)
(-4,3)
(2,0)
36a - 6b + c = 0
16a -4b + c = 3
4a + 2b + c = 0
c = -4a - 2b
36a - 6b - 4a -2b = 0
16a - 4b -4a - 2b = 3
32a -8b = 0
12a - 6b = 3
4a - b = 0
4a - 2b = 1
b = -1
4a + 1 = 0
4a = -1
a = -1/4
c = 1 + 2 = 3
y = -1/4x^2 - x + 3
Answer:
Step-by-step explanation:
y = ax² + bx + c
( - 6)²a - 6b + c = 0 ⇒ 36a - 6b + c = 0
( - 4)²a - 4b + c = 3 ⇒ 16a - 4b + c = 3
2²a + 2b + c = 0 ⇒ 4a + 2b + c = 0
A = [tex]\left[\begin{array}{ccc}36&-6&1\\16&-4&1\\4&2&1\end{array}\right][/tex] = - 96
[tex]A_{a}[/tex] = [tex]\left[\begin{array}{ccc}0&-6&1\\3&-4&1\\0&2&1\end{array}\right][/tex] = 24
[tex]A_{b}[/tex] = [tex]\left[\begin{array}{ccc}36&0&1\\16&3&1\\4&0&1\end{array}\right][/tex] = 96
[tex]A_{c}[/tex] = [tex]\left[\begin{array}{ccc}36&-6&0\\16&-4&3\\4&2&0\end{array}\right][/tex] = - 288
a = [tex]\frac{A_{a} }{A}[/tex] = [tex]\frac{24}{-96}[/tex] = - [tex]\frac{1}{4}[/tex]
b = [tex]\frac{A_{b} }{A}[/tex] = - 1
c = [tex]\frac{A_{c} }{A}[/tex] = 3
y = - [tex]\frac{1}{4}[/tex] x² - x + 3
