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{ =- }(b^(2)-4ac)/(4a)`
`\begin{gathered} yv\text{ = -}(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{ = -}(b)/(2a)`
`\begin{gathered} xv\text{ =- }(4)/(2(-2)) \\ xv\text{ = }(-4)/(-4) \end{gathered}`

xv = 1

Vertex:

(xv , yv ) = (1 , 4 )

The answer is:

The vertex of the parabola is (1 , 4)