Question

Functions 1 and 2 are shown below: Function 1: f(x) = −3x2 + 2 A graph of a parabola with x intercepts of negative 0.5, 0 and 2, 0 and a vertex of 0.5, 4 is shown. Which function has a larger maximum? Type your answer as 1 or 2.

Answer 1

2. i belive the answer should be

Answer 2

The maximum value of function 1 is 2 and maximum value of function 2 is 4. So, function 2 has a larger maximum.

Explanation:

In Function 1 :

`f(x)=-3x^2+2`

Lending coefficient is negative. It is a downward parabola and vertex is the maximum point.

vertex of a parabola
`ax^2+bx+c=0` is

`vertex=((-b)/(2a),f((-b)/(2a)))`

On comparing with given equation we ave;

a = -3 , b=0 and c = 2

then;

`x =(-0)/(2(-3)) =0`

Substitute the value of x =0 in
`f(x)=-3x^2+2` we have;

`f(0)=-3(0)^2+2=0+2 = 2`

⇒Vertex = (0, 2)

⇒the maximum value of function 1 is 2.

In Function 2:

Vertex = (0.5, 4)

⇒the maximum value of function 2 is 4.

Therefore, Function 2 has a larger maximum.