```Question 114163
To get the point on the y axis where the graph crosses, set the value of x at zero and solve
the equation for the corresponding value of y. [Note that for any point on the y-axis the
value of x for that point is zero.] So to find the value of the y-intercept, you go to the
equation:
.
{{{y = x^2 + 6x + 8}}}
.
and set x = 0 to get that:
.
{{{y = 0^2 + 6*0 + 8}}}
.
The first two terms on the right side equal zero so the equation reduces to:
.
{{{y = 8}}}
.
This means the graph crosses the y-axis at +8 on the y-axis.
.
Similarly you can find the values where the graph crosses the x-axis by setting y equal to zero
because any coordinate point on the x-axis has zero for its y value. Setting y equal to zero
in the equation leads to:
.
{{{0 = x^2 + 6x + 8}}}
.
and transposing this equation (switching sides just to get it into a little more familiar
format) results in:
.
{{{x^2 + 6x + 8 = 0}}}
.
Notice that the left side can be factored to convert the equation to:
.
{{{(x + 4)(x + 2) = 0}}}
.
[You can multiply out the left side, just to make sure we factored it correctly, if you would
like to.]
.
This factored form will be correct if either of the factors is equal to zero, because if
either factor is zero, the left side will involve a multiplication by zero ... and this
makes the entire left side equal to zero and therefore equal to the right side.
.
So set each of the factors equal to zero. First:
.
{{{x + 4 = 0}}}
.
which, by subtracting 4 from both sides, becomes:
.
{{{x = -4}}}
.
Then, set:
.
{{{x + 2 = 0}}}
.
which, by subtracting 2 from both sides, becomes:
.
{{{x = -2}}}
.
This tells us that the x-axis intercepts cross the x-axis at -4 and -2.
.
The graph for the original equation is:
.
{{{graph(600,600,-15,15,-15,15,x^2+6x+8)}}}
.
Notice where the x and y axis intercepts are. They match the work that we did.
.
Hope this helps you to understand the problem and how to get the answers.
.
```