here we're asked to graph a quadratic
function, the first step is to determine
the y intercept the y intercept occurs
when x is 0 so when x is 0 here y you
can easily see should be 2 the next step
is to determine the x-intercepts in this
case you find the x-intercepts when y is
equal to 0 so 0 equals x squared plus 2
subtracting 2 and solving this quadratic
we can extract the root here don't
forget the plus or minus when you do
that but notice what happens here I'm
left with plus or minus I times the
square root of 2 ok when the
x-intercepts turn out to be imaginary
there's that's telling me the math is
telling me there's no X intercepts all
parabolas have a vertex so the vertex
while the x-value of the vertex can be
gotten with the formula negative B over
2a
in this particular case notice a is 1 B
is 0 and C is 2 so when I plug in 0
negative 0 over 2 times a well 0 divided
by anything is just 0 so when x is 0 the
corresponding Y value would be 2 0
squared is just 0 so 0 squared plus 2 is
2 so the vertex is a 0 comma 2
notice here the vertex is the same as
the y-intercept you'll see later when we
have our transformations here we have a
regular a basic graph here parabola
shifted up 2 units so we only really
have one point you know one point is not
enough to graph a parabola so at this
point we're sort of stuck let's go ahead
and make a chart of values and let's get
a couple more here so let's say we have
negative one we already know if we plug
in 0 we'll get
- and let's look at what happens when X
is 1 so when y is negative 1
substituting that in negative 1 squared
+ 2 is 3 okay so the score corresponding
Y value there would be 3 now let's do
the same thing by plugging in when we
plug in 1 there 1 squared is 1 and there
I get 3 as well ok so here's 3 points at
least we know the parabola also opens up
because the leading coefficient is
positive so let's graph this okay so 0
comma 2 is the y-intercept and also the
vertex 1 comma 3 and negative 1 comma 3
so here's the parabola you can sort of
see it here where the line of symmetry
is the Y axis let me go ahead and
connect the dots well here you go this
is the best I can do on the computer
here you notice the parabola opening up
there's my y intercept which also
happens to be the vertex at 0 comma 2
and no x-intercepts notice here the math
told us that right we got here an
imaginary x intercept so it's telling me
no x-intercepts in this case so there it
is y equals x squared plus 2
