Question

The table shows several input and output values of a quadratic function f(x)

x f(x)
3.0 3.00
4.0 5.00
4.5 5.25
5.0 5.00
6.0 3.00

Which statements is tru about the function?
a) The maximum value of f(x) is 6
b) The maximum value of f(x) is 5.25
c) The zeroes of the function are 2 and 4
d) The zeroes of the function are 4 and 5

Answer 1

Answer:-by-step explanation:

the function has the x-intercept of (-2, 0)

the function has the y-intercept of (0, -8)

the function has the x-intercept of (4, 0)

Answer 2

the correct statement about the function is:

b) The maximum value of
`\( f(x) \)` is 5.25.

Given the data points for the quadratic function
`\( f(x) \)`:

-
`\( x = 3.0, f(x) = 3.00 \)`

-
`\( x = 4.0, f(x) = 5.00 \)`

-
`\( x = 4.5, f(x) = 5.25 \)`

-
`\( x = 5.0, f(x) = 5.00 \)`

-
`\( x = 6.0, f(x) = 3.00 \)`

We can analyze the statements provided:

a) The maximum value of
`\( f(x) \)` is 6:

- This is not true based on the given values because the highest
`\( f(x) \)` value is 5.25.

b) The maximum value of
`\( f(x) \)` is 5.25:

- This statement appears to be true because, among the provided
`\( f(x) \)` values, 5.25 is the largest.

c) The zeroes of the function are 2 and 4:

- There is no data provided for
`\( x = 2 \)`, so we cannot confirm that the function has a zero at
`\( x = 2 \)`. Moreover,
`\( f(x) \)` is not zero when
`\( x = 4 \)`; therefore, this statement is false.

d) The zeroes of the function are 4 and 5:

- The given data points do not include a zero value of
`\( f(x) \)` for
`\( x = 4 \)` or
`\( x = 5 \); \( f(x) \)` is 5.00 for both these
`\( x \)`-values, so this statement is false.

Based on the provided data, the correct statement about the function is:

b) The maximum value of
`\( f(x) \)` is 5.25.