Sketch the graph of x^2 + 4x + 3

Although this sounds like a complex problem, we can simplify it down to just finding the roots of the equation. Let's start by drawing a standard x^2 curve (would draw). We can see that it goes through the (0,0) point which makes sense as if we enter the value x = 0 into the equation, we get out 0. We can do the same thing to find where the graph crosses the y axis, be considering the value of x when y = 0. To do this, we need to solve the equation - we can do this by factorisation. When factorising, we want to find the two numbers that multiply together to get 3 and add together to get 4. In this case that would be 3 and 1. Therefore the equation is now:(x+1)(x+3) and we are trying to find where this equals zero. We can do that by making each bracket equal zero so we find x = -1 and x = -3. Now we know the graph passes through the -1 and -3 points so we can now sketch it (would sketch).