Question

How do you determine whether the graph of `y = x^2 + 6x − 5` opens up or down and whether it has a maximum or minimum point?

Answer 1

`"see explanation"`

Explanation:

`"given the equation of a parabola in "color(blue)"standard form"`

`•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0`

`• " if "a>0" then graph opens up and is a minimum"`

`• " if "a<0" then graph opens down and is a maximum"`

`y=x^2+6x-5" is in standard form"`

`"with "a=1>0`

`rArr"graph opens up and is a minimum"`
graph{x^2+6x-5 [-40, 40, -20, 20]}