# What is the vertex of  y=-3x^2+5x+6?

Jun 20, 2017

$0.833 , 8.083$

#### Explanation:

The vertex can be found using differentiation, differentiating the equation and solving for 0 can determine where the x point of the vertex lies.

$\frac{\mathrm{dy}}{\mathrm{dx}} \left(- 3 {x}^{2} + 5 x + 6\right) = - 6 x + 5$
$- 6 x + 5 = 0 , 6 x = 5 , x = \frac{5}{6}$

Thus the $x$ coordinate of the vertex is $\frac{5}{6}$
Now we can substitute $x = \frac{5}{6}$ back into the original equation and solve for $y$.

$y = - 3 {\left(\frac{5}{6}\right)}^{2} + 5 \left(\frac{5}{6}\right) + 6$
$y = 8.0833$

Jun 20, 2017

$\left(\frac{5}{6} , \frac{97}{12}\right)$

#### Explanation:

$\text{for a parabola in standard form } y = a {x}^{2} + b x + c$

"the x-coordinate of the vertex is " x_(color(red)"vertex")=-b/(2a)

$y = - 3 {x}^{2} + 5 x + 6 \text{ is in standard form}$

$\text{with } a = - 3 , b = 5 , c = 6$

$\Rightarrow {x}_{\textcolor{red}{\text{vertex}}} = - \frac{5}{- 6} = \frac{5}{6}$

$\text{substitute this value into the function for y-coordinate}$

$\Rightarrow {y}_{\textcolor{red}{\text{vertex}}} = - 3 {\left(\frac{5}{6}\right)}^{2} + 5 \left(\frac{5}{6}\right) + 6 = \frac{97}{12}$

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(\frac{5}{6} , \frac{97}{12}\right)$

Jun 20, 2017

$\left(\frac{5}{6} , \frac{97}{12}\right)$

#### Explanation:

$y = a {x}^{2} + b x + c$ [Standard Form of a Quadratic Equation]
$y = - 3 {x}^{2} + 5 x + 6$

$a = - 3$
$b = 5$
$c = 6$

TO FIND THE X-VALUE OF THE VERTEX:
Use the formula for the axis of symmetry by substituting values for $b$ and $a$:
$x = \frac{- b}{2 a}$
$x = \frac{- 5}{2 \left(- 3\right)}$
$x = \frac{- 5}{-} 6$
$x = \frac{5}{6}$

TO FIND THE Y-VALUE OF THE VERTEX:
Use the formula below by substituting values for $a$, $b$, and $c$:
$y = \frac{- {b}^{2}}{4 a} + c$
$y = \frac{- {\left(5\right)}^{2}}{4 \left(- 3\right)} + 6$
$y = \frac{- 25}{- 12} + 6$
$y = \frac{25}{12} + \frac{72}{12}$
$y = \frac{97}{12}$

Express as a coordinate.
$\left(\frac{5}{6} , \frac{97}{12}\right)$