Question

I did graph number one and now I need help with graph number two. I'm also asking if u can help me answer the two bottom questions.
I might give u the brainliest answer

Answer 1

Hello!

I noticed a mistake in your first question: For the value of x = -4, when you squared the negative number, it should've become positive, as a negative number * a negative number = a positive.

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First, let's solve the table. The equation you are supposed to solve is $y = (x-3)^{2}$. To solve these, substitute in the value of x and solve for y.

x=1: $y = (1-3)^{2}$

$y = (-2)^{2}$

y = 4

x=2: $y = (2-3)^{2}$

$y = (-1)^{2}$

y = 1

x=3: $y = (3-3)^{2}$

$y = (0)^{2}$

y = 0

And so on. Once you solve these, graph the points. I attached a quick drawing I made of what it should look like.

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Your next question: How does the graph of y = x² - 2 differ from y = x²? How does the graph of y = x² + 2 differ from y = x²?

The difference here is the addition and subtraction of the value of 2. When you add or subtract a number on the outside of an equation, this moves the equation up and down.  Adding a number moves it up by that number, and subtracting moves it down. y = x² - 2 therefore differs from y = x² because it is moved down by two units, and y = x² + 2 because it is moved up by two units.

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Your next question: How does the graph of y = (x - 2)² differ from y = x²? How does the graph of y = (x + 2)² differ from y = x²?

The difference here is also the addition and subtraction of the value of 2. However, the difference between this and the previous question is the values are added on the inside of an equation. This moves the equation left and right, however, in this case, adding moves it left, and subtracting moves it right. y = (x - 2)² therefore differs from y = x² because it is moved right by two units, and y = (x - 2)² because it is moved left by two units.

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Hope this helps!