Question

Mathieu is finding the x-intercepts of the function f(x)=x^2+4x+3. His world is shown below. (In the photo) The Answer is: (He set the factored expressions equal to each other) I learned that the hard way trial and error >~< Which error did Mathieu make? He factored incorrectly. He did not use the constant as the x-intercept. (He set the factored expressions equal to each other.) He incorrectly solved the equation x + 3 = x + 1.

Answer 1

Answer: he set the factored expressions equal to each other.

Answer 2

X intercepts are points where a function intersects or cuts through the x axis where y=0.

Explanation:

In the function given which is f(x) =x^2 +4x + 3 we see that this is a parabola of which when the graph is drawn it has a U shape so when finding x intercepts of this function it is those points on the function where the graph cuts the x axis and at those two points f(x)= 0, so here Mathieu had made a mistake of factorizing and equating the x intercepts for this function.

For finding the X intercepts let f(x) = 0

therefore 0= x^2 + 4x + 3 now we solve for x

0= (x+1)(x+3)

(x+1)= 0 or (x+3)=0

therefore x=-1 or x=-3

now if you substitute these values onto the function they give f(x)= 0,

f(-1) = (-1)^2 + 4(-1) + 3 = 0

f(-3) = (-3)^2 + $(-3) + 3 =0

now let us look at Mathieus answer which is x+1 = x+3 yes these x values do give the same y value but they are not equal because if you can actually solve this further you would not get a defined answer. Both these are factors of the function but are not actually equal as the function would not be able to be drawn if this was the case.