Question

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

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

$Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)$

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, $a=-2,b=10,c=-7$.

$\dfrac{-b}{2a}=\dfrac{-10}{2(-2)}$

$\dfrac{-b}{2a}=\dfrac{-10}{-4}$

$\dfrac{-b}{2a}=\dfrac{5}{2}$

Putting $x=\dfrac{5}{2}$ in (i), we get

$y=-2(\dfrac{5}{2})^2+10(\dfrac{5}{2})-7$

$y=-2(\dfrac{25}{4})+\dfrac{50}{2}-7$

$y=\dfrac{-50}{4}+25-7$

$y=\dfrac{-25}{2}+18$

On further simplification, we get

$y=\dfrac{-25+36}{2}$

$y=\dfrac{11}{2}$

So, the vertex of the given quadratic equation is $\left(\dfrac{5}{2},\dfrac{11}{2}\right)$.

Therefore, the correct option is A.