If the blue graph is the parent function, write an equation representing the red graph.

Question

blue is at 0,0 And i have to write an equation For -6,0

Answer 1

So while this probem gives you very little information, It actually becomes quite easy once you maser the concept of shifting graphs horizontally and vertically and compressing graphs and stretching. Becuase the blue graph is the parent graph of the red graph, we know that the red graph must be in the same basic formula i.e if the blue graph is y=x, the red graph would have a similar form such as y=Ax+ B with A and B being constants, or if the blue graph was y=x^2 the red graph would be something like A(x+B)^2 +C. with A B and C being constants. Because the solution or X intercept of the blue graph is at x=0 and the other is at x=-6, we can see that this must be at least horizontal shift. More specifically this is a horizontal shift to the left, so in order to do this we offset the graph by 6. if the blue graph is y=x the red one must be is y=(x+6) if the blue graph is y= x^2, the blue graph would be y=(x+6)^2 if you plug in any of these functions you will find that they fit the 2 intercepts you spoke about in your question.

Answer 2

Assuming we're talking about parent functions and transformations.

If you were working with something like y = (x)², you would need to change the function to read y = (x + 6)² in order to move the function to the left by 6.