# What is the vertex form of y=-2x^2+17x+13 ?

Dec 29, 2015

The co-ordinate of vertex is $\left(4.25 , 49.125\right)$

#### Explanation:

The general form of Parabola is $y = a \cdot {x}^{2} + b \cdot x + c$
So here a=-2 ; b=17 ; c=13#
We know the x co-ordinate of the vertex is $\left(- \frac{b}{2} a\right)$
Therefore the x co-ordinate of the vertex is $\left(- \frac{17}{-} 4\right)$ or $4.25$
Since the parabola passes through vertex the y co-ordinate will satisfy the above equation. Now putting $x = \frac{17}{4}$ the equation becomes $y = - 2 \cdot {17}^{2} / {4}^{2} + 17 \cdot \frac{17}{4} + 13$ or $y = 49.125$
Thus the co-ordinate of vertex is $\left(4.25 , 49.125\right)$[answer]