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Here's a graph of

y = (x – 3)(x + 3) red
y = (x – 4)(x + 2) blue

Where is red graph "under" the blue graph?

https://www.desmos.com/calculator/qeguhei7df

It's under whenever x < 1/2.

Be very careful of how you're stating each piece...it's not really "function 3" - they're all pieces of the same singular function, it's just that the function does different things based on the restrictions to the domain.

For the leftmost piece, the 3 is fairly obvious. For the other ones, you can see that they are linear functions; you can do point-slope form [y - y1 = m(x - x1) ]or slope-intercept [y = mx + b] form for both pieces.

The last one, I actually just noticed there are 3 points that match on the graph exactly: (1,2), (2,1), and (3,-2). I just put those into a table and ran a Quadratic Regression against it (see the link) https://www.desmos.com/calculator/kw9dutw2jd

This book really helped me out. I had to essentially lean a lot of algebra my self in middle school and in high school. I have the 3rd edition but this 4th edition and she gives you examples. https://www.amazon.com/Forgotten-Algebra-Barbara-Bleau-Ph-D/dp/1438001509

Sorry, but I think you'll find your daughter is confused. That is a perfectly acceptable line to graph. Don't stress though. I've just gone back to highschool & can understand her confusion! She'll realise when she goes to school. Btw, I've included a site that will show you the graph. https://www.desmos.com/calculator Make sure you put 7x/4 + 4 :).

What you'll see is the horizontal line is the x line. To find the x intercept make y = 0. So

0 = 7x/4 + 4.

Move the 4 to the other side of the equation.

-4 = 7x/4.

Times both sides by 4.

-16 = 7x.

Divide both sides by 7.

-16/7 or -2.2857 = x.

(When you move a number to the other side of the equation you always want to do the opposite of what it is already doing.)

The vertical line is the y line. To find where the y intercept is make x = 0.

y = 7*0/4 + 4.

Because 7*0 = 0 you are therefore trying to divide 0 by 4 which you cannot do so.

y= +4.

You'll see that's where the graph crosses the y line.

Hope this helps!

So, I plugged this equation into Desmos and found the intersection between the lines of each side. Here it is.

The solution, to eight places, is x = 0.93945499, though I imagine you would probably round it to about 0.93950.