Question

looking to recieve help with finding the vertex of the parabola.

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

f(x) = - 2x² + 4x + 2

Step 02:

y = ax² + bx + c

a = -2

b= 4

c = 2

vertex of the parabola equation

$yv\text{ =- }\frac{b^{2}-4ac}{4a}$$\begin{gathered} yv\text{ = -}\frac{4^2-4\cdot(-2)\cdot(2)}{4\cdot(-2)} \\ yv\text{ = -}\frac{(16+16)_{}}{-8} \end{gathered}$

yv = (- 32) / (- 8)

yv = 4

$xv\text{ = -}\frac{b}{2a}$$\begin{gathered} xv\text{ =- }\frac{4}{2(-2)} \\ xv\text{ = }\frac{-4}{-4} \end{gathered}$

xv = 1

Vertex:

(xv , yv ) = (1 , 4 )

The answer is:

The vertex of the parabola is (1 , 4)