Jacob and Zachary go to the movie theater and purchase refreshments for their friends. Jacob
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Using the given information we found that the equation of the parabola is:
y = (-4/9)*(x - 3)^2 + 5
And its graph is below.
<h3>How to get the equation of the parabola?</h3>
For a parabola with vertex (h, k), the equation is:
y = a*(x - h)^2 + k
Here the vertex is (3, 5), so the equation is:
y = a*(x - 3)^2 + 5
And the y-intercept is y = 1, this means that:
1 = a*(0 - 3)^2 + 5
1 = a*9 + 5
1 - 5 = a*9
-4/9 = a
So the parabola is:
y = (-4/9)*(x - 3)^2 + 5
And its graph is below.
If you want to learn more about parabolas, you can read:
Let's take a look at a perfect square trinomial.
We can distribute this expression to get
.
An important relation to recognize here is that the constant is the square of half of the x value.
Now, if we wanted to add a number to
to make a perfect square trinomial, we could have the value of x and then square it.
Half of 16 is 8, and 8 squared is
We can distribute this expression to get
An important relation to recognize here is that the constant is the square of half of the x value.
Now, if we wanted to add a number to
Half of 16 is 8, and 8 squared is