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Question

Hi there! My name is Cam and for my distance learning, I’m struggling with the new concept of quadratics in my 8th grade algebra class. My new teacher for this class has not responded to any messages or anything. I’m lost and I need help.

Here’s what I need help with: Write an equation to represent the relationship between the step number and the number of squares.

Image: https://photos.app.goo.gl/jztNBchRL5NJNVLw5

The question below says: Is the relationship between the step number and the number of squares a quadratic function? Explain your reasoning.

Thank you!

Answer 1

Hi Cam,

A quadratic is just a formula with a 2 exponent, something like this: y=3x²+2x+18.

In this case, finding the number of squares is like finding the area.

There are 2 parts to each of these diagrams, the square, and the line.

The order number for each picture is what we will call x. (x=1 for the first one, x=2 for the second one, x=3 for the third one)

First, you want to find the equation that represents the squares. As you probably know, the area of a square is its length multiplied by itself, or length * length. We can represent this using the formula x*x, where x is the length of the square. x*x can also be written as x². You can see that the area of the first one has 1 square (1²=1), the second one has 4 squares (2²=4) and the third has 9 squares (3²=9).

Second, you want to find the equations that represent the lines of squares below them. The number of squares is equal to the order number of the picture, as the first one has 1 square, the second one has 2 squares, and the third one has 3 squares. Therefore, the area for this part will be equal to x.

Putting these two parts together, the area (or number of squares) will be x²+x, which would be written out at y=x²+x.

This equation, or relationship, is quadratic because it contains an x²

Answer 2

Cam-

try X^2 + X