Give an example of a quadratic function has a maximum value. explain how you know it has a maximum algebraically

y = -x²  

Step-by-step explanation:

The simplest quadratic I can think of is

y = -x²

It must have a maximum because as

x ⟶  -∞, y ⟶ -∞ and as

x ⟶ +∞, y ⟶ -∞.

There must be a maximum somewhere between the two extremes.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

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