### Video Transcript

Write the quadratic equation
represented by the graph shown.

We begin by observing the general
shape of the given graph. It is a parabola, meaning that it
is the graph of a quadratic function and it has a line of symmetry given by the
π¦-axis or the equation π₯ equals zero. This means its equation will be of
the form π of π₯ equals π times π₯ squared plus π, with π not equal to zero.

Our job now will be to identify the
values of π and π. We recall that the π¦-intercept of
the function is found by calculating π of zero. For an equation of the form π of
π₯ equals π times π₯ squared plus π, we find that π of zero equals π. The quadratic graph shown has a
π¦-intercept of two. Thus, π equals two. This allows us to write our
equation as π of π₯ equals π times π₯ squared plus two.

Next, we can calculate the value of
π by choosing any point that lies on the given parabola. Letβs choose two, negative two. This tells us that π of two equals
negative two. We will proceed by substituting two
for π₯ in our equation. By simplifying, we show that π of
two equals four π plus two. To solve for π, we will use the
fact that π of two also equals negative two from the graph. This gives us the equation negative
two equals four π plus two. To solve this equation, we subtract
two from each side of the equation. Then, we divide by four. The result is π equals negative
one. In fact, we would expect π to be
less than zero since the parabola opens down, or is n shaped.

Now that we know that π equals two
and π equals negative one, we can write the equation for the given quadratic
graph. The quadratic equation represented
by the graph shown is π of π₯ equals negative π₯ squared plus two.