Answer:
b = -84
c = 285
Step-by-step explanation:
Given that:
[tex]g(x)=6x^2+bx+c[/tex]
Vertex of (7, -9).
To find:
Value of b and c = ?
Solution:
It can be seen that the given equation is of a parabola.
Standard equation of a parabola is given as:
[tex]y =Ax^2+Bx+C[/tex]
x coordinate of vertex is given as:
[tex]h=\dfrac{-B}{2A}[/tex]
Here, A = 6, B = b and C = c, h = 7 and k = -9
[tex]7=\dfrac{-b}{2\times 6}\\\Rightarrow b = -84[/tex]
So, the equation of given parabola becomes:
[tex]y=6x^2-84x+c[/tex]
Now, putting the value of vertex in the equation to find c.
[tex]-9=6\times 7^2-84\times 7+c\\\Rightarrow -9=294-588+c\\\Rightarrow -9=-294+c\\\Rightarrow c = 285[/tex]
So, the answer is :
b = -84
c = 285
