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dsp73
3 years ago
13

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

Mathematics
1 answer:
Blizzard [7]3 years ago
7 0

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

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