3x^2-11x-4=y
We have the form
Ax^2 + Bx + C = y
The x coordinate of the vertex is given by : -B/ (2A) = - (-11) / (2*3) = 11/6
To find the y coordinate.....put this x value back into the function....and we have
3(11/6)^2 - 11(11/6) - 4
3(121/36) - 121/6 - 4
121/12 - 121/6 - 4
121/12 - 242/12 - 48/12 =
-169/12
So....the vertex is ( 11/6, -169/12 )
3x^2-11x-4=y
We have the form
Ax^2 + Bx + C = y
The x coordinate of the vertex is given by : -B/ (2A) = - (-11) / (2*3) = 11/6
To find the y coordinate.....put this x value back into the function....and we have
3(11/6)^2 - 11(11/6) - 4
3(121/36) - 121/6 - 4
121/12 - 121/6 - 4
121/12 - 242/12 - 48/12 =
-169/12
So....the vertex is ( 11/6, -169/12 )
what is the vertex of this equation 3x^2-11x-4=y
Formula:
\(\begin{array}{|rcll|} \hline ax^2+bx+c &=& 0 \\\\ x_v &=& -\frac{b}{2a} \\ y_v &=& c - \frac{b^2}{4a} \\ \hline \end{array}\)
Vertex:
\(\begin{array}{|rcll|} \hline y &=& 3x^2-11x-4 \quad & | \qquad a = 3 \qquad b=-11 \qquad c = -4 \\\\ x_v &=& -\frac{(-11)}{2\cdot 3} \\ &=& \frac{11}{6} \\ \mathbf{x_v} &\mathbf{=}& \mathbf{1.8\bar{3}} \\\\ y_v &=& -4 - \frac{(-11)^2}{4\cdot 3} \\ &=& -4 - \frac{121}{12} \\ &=& -\frac{169}{12} \\ \mathbf{y_v} &\mathbf{=}& \mathbf{-14.08\bar{3}} \\ \hline \end{array}\)