Write the equation of the function whose graph is shown. What is the equation?

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Answer 1 · 2017-07-01T03:37:37

$y = (x-5)^2 + 3$

This graph is a parabola.

We can see that the vertex is given: it is $(5,3)$ .

The vertex form of a parabola with vertex $(h,k)$ looks like this:

$y = a(x-h)^2+k$

So in this case, we know that our formula will look like this:

$y = a(x-5)^2+3$

Now, we can plug in the other point we were given and solve for $a$ :

$12 = a(8-5)^2+3$

$9 = a(3)^2$

$9 = 9a$

$1 = a$

Therefore, the equation for the parabola looks like this:

$y = (x-5)^2 + 3$

Final Answer