Do you agree with the statement that " cubic functions must have at least 1 x-intercept but not more than 3, whereas quadratic functions may or may not have x-intercepts

Yes, I agree

Step-by-step explanation:

For the cubic function

A cubic function is represented as:

A cubic function may have 1, 2 or 3 x intercepts. This is shown below

For 3 x intercepts

Equate y to 0

Expand

Express as difference of two squares

x = 0 or 1 or -1

For 2 x intercepts

Equate y to 0

Expand

x= 5 or x = -7

For 1 x intercept

Equate y to 0

Take cube roots of both sides

It has been shown above that a cubic function may have 1, 2 or 3.

So, I agree to the statement

For the quadratic function

A quadratic function will not have any x intercept when the function can not be factorized;

E.g.

The above function has no x intercept.

A quadratic function will have at least 1 x intercept when the function can be factorized;

E.g.

Equate y to 0

Expand

We've shown that a quadratic may have no x intercept, and it may also have x intercept(s)

Hence, I agree to both statement

1. 22

2. 1

3. 7

4. 18

step-by-step explanation

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