Question

Find the values of b and c so g(x)=6x^2+bx+c has a vertex of (7,-9).

Answer 1

Answer:

b = -84

c = 285

Step-by-step explanation:

Given that:

$g(x)=6x^2+bx+c$

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:

$y =Ax^2+Bx+C$

x coordinate of vertex is given as:

$h=\dfrac{-B}{2A}$

Here, A = 6, B = b and C = c, h = 7 and k = -9

$7=\dfrac{-b}{2\times 6}\\\Rightarrow b = -84$

So, the equation of given parabola becomes:

$y=6x^2-84x+c$

Now, putting the value of vertex in the equation to find c.

$-9=6\times 7^2-84\times 7+c\\\Rightarrow -9=294-588+c\\\Rightarrow -9=-294+c\\\Rightarrow c = 285$

So, the answer is :

b = -84

c = 285