Answer to Question #160742 in Algebra for Jkkl

Question

compare and contrast quadratic and exponential function (using visuals/diagrams) . In your discussion, consider using the following talking points: first differences, quadratic, exponential, equation, graph, f(x)=x^2, f(x)=2^x. 

Answer 1

Firstly, quadratic function is a polynomial with the highest degree of 2. That is, $x^2$ is always present there. While, exponential function has a variable as it exponent e.g. $2^x$.

Differences:

When the independent variable changes by a constant amount, quadratic functions have constant second differences, while exponential functions have a constant ratio.

Graph:

Taking $f(x)=x^2$ and $f(x)=2^x$ to be the example for quadratic and exponential function respectively. We see the graph as follows

This is the graph of $f(x)=x^2$

This is the graph of $f(x)=2^x$

We see that the quadratic graph makes/form a Parabola (whether facing up or down). While the exponential function graph rises or falls freely in One Direction.