Question

Give the properties for the equation -2x 2 - y + 10x - 7 = 0.

>Vertex

(5/2, 11/2)
(-5/2, 11/2)
(5, -7)

Answer 1

Given:

The quadratic equation is

`-2x^2-y+10x-7=0`

To find:

The vertex of the given quadratic equation.

Solution:

If a quadratic function is
`f(x)=ax^2+bx+c`, then

`Vertex=\left((-b)/(2a),f((-b)/(2a))\right)`

We have,

`-2x^2-y+10x-7=0`

It can be written as

`-2x^2+10x-7=y`

`y=-2x^2+10x-7` ...(i)

Here,
`a=-2,b=10,c=-7`.

`(-b)/(2a)=(-10)/(2(-2))`

`(-b)/(2a)=(-10)/(-4)`

`(-b)/(2a)=(5)/(2)`

Putting
`x=(5)/(2)` in (i), we get

`y=-2((5)/(2))^2+10((5)/(2))-7`

`y=-2((25)/(4))+(50)/(2)-7`

`y=(-50)/(4)+25-7`

`y=(-25)/(2)+18`

On further simplification, we get

`y=(-25+36)/(2)`

`y=(11)/(2)`

So, the vertex of the given quadratic equation is
`\left((5)/(2),(11)/(2)\right)`.

Therefore, the correct option is A.