Show that 6 – 4x - x^2 can never be greater than 10. ( This is an Additional Math Question )

Mathematics

1 answer:

notsponge [240]3 years ago

7 0

Answer:

see explanation

Step-by-step explanation:

Given

6 - 4x - x²

Since the coefficient of the x² term < 0 then parabola has a maximum vertex.

To find the x- coordinate of the vertex

$x_{vertex}$ = - $\frac{b}{2a}$

with a = - 1 and b = - 4 , then

$x_{vertex}$ = - $\frac{-4}{-2}$ = - 2

The corresponding y- coordinate is found by substituting x = - 2 , that is

6 - 4(- 2) - (- 2)² = 6 + 8 - 4 = 10

vertex = (- 2, 10 )

The maximum value of the function is the y- coordinate of the vertex

Then maximum value is 10

Thus 6 - 4x - x² is never greater than 10

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