What does the coefficient of the variable of 4x^2+9 mean in terms of this problem

Answer 1

The coefficient of the leading term in a parabola, tells you if the parabola opens Upward or Downward, and if the parabola is horizontally Compressed, Stretched or neither.

Parabola: ax² + bx + c

a > 0 opens Upward

a < 0 opens Downward

| a | > 1 Compresses

| a | < 1 Stretches

| a | = 1 it doesn't change

In this case:

4x² + 9

(2x)² + 9

The leading coefficient tell us:

a = 2

2 > 1 The parabola opens Upward

| 2 | >1 The parabola Horizontally Compresses by a factor of 2

Answer 2

What is a coefficient?

A coefficient is the number that precedes(or comes before )a variable.

For example, in –2x , –2 is the coefficient of x ;

In 7y², 7 is the coefficient of y².

I hope this helps you to answer your question.