Question

Which of the following equations represents a graph that increases the most rapidly?

Answer 1

I would imagine it would be the first one because the coefficient of 4 has the greatest effect out of all of them

Answer 2

Answer:

A . $y =4x^{2} +10x -6$

Step-by-step explanation:

Here the degree of all equations (polynomial) are 2 but the leading coefficient of $x^{2}$ in all equation are different which are the following.

(1). The leading coefficient of $x^{2}$ in the equation $y =4x^{2} x^{2} +10x-6$ is 4.

(2). The leading coefficient of $x^{2}$ in the equation $y =3x^{2}  +15x+18$ is 3.

(3). The leading coefficient of $x^{2}$ in the equation $y =2x^{2} -x -15$ is 2.

(4). The leading coefficient of $x^{2}$ in the equation $y= \frac{1}{2} x^{2} -\frac{5}{2} x-12$ is 0.5.

In the above four equations the leading coefficient of $x^{2}$ is greatest in the equation $y=4x^{2}  +10x-6$ .

Hence the graph of $y =4x^{2} +10x -6$is increases most rapidly.