Question

Determine whether f(x) = –5x^2 – 10x + 6 has a maximum or a minimum value.

Answer 1

First,

We are dealing with parabola since the equation has a form of,

$y=ax^2+bx+c$

Here the vertex of an up - down facing parabola has a form of,

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

The parameters we have are,

$a=-5,b=-10, c=6$

Plug them in vertex formula,

$x_v=-\dfrac{-10}{2(-5)}=-1$

Plug in the $x_v$ into the equation,

$y_v=-5(-1)^2-10(-1)+6=11$

We now got a point parabola vertex with coordinates,

$(x_v, y_v)\Longrightarrow(-1,11)$

From here we emerge two rules:

• If $a$ then vertex is max value
• If $a>0$ then vertex is min value

So our vertex is minimum value since,

$a=-5\Longleftrightarrow a$

Hope this helps.

r3t40