Question

Compare the algebraically expressed function f(x) = -8x2 + 4x + 2 to the function shown in the graph to determine which statement is true.

A) The algebraic function has a greater maximum value.
B) The algebraic function has a lower minimum value.
C) The graphed function has a greater maximum value.
D) The graphed function has a lower minimum value.

Answer 1

Option A.

Explanation:

Algebraically expressed function is f(x) = -8x² + 4x + 2

As we know in a quadratic equation f(x) = ax² + bx + c, if a is negative then the vertex will be maximum.

and the maximum value will be represented by
`c-(b^(2))/(4a)`

From the given quadratic equation

a = -8

b = 4 and c = 2

Now we place these values in the equation.

Maximum =
`2-(4^(2))/(4(-8))`

= 2 + 0.5

= 2.5

From the graph attached we can easily conclude that vertex of the parabola is less than 0.5

Therefore, algebraic function has the greater maximum value.

Option A. is the answer.

Answer 2

A) The algebraic function has a greater maximum value.

EXPLANATION

The given function is

`f(x) = - 8 {x}^(2) + 4x + 2`

This can be rewritten as:

`f(x) = - 8( {x - (1)/(4) })^(2) + (5)/(2)`

The maximum value of this function is 2.5

The maximum value of the graph is less that zero.

This means that that the maximum value of the algebraic function is greater than the maximum value of the graph.