Given the following graph of a parabola, find its equation, in the form

Question

𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘

Answer 1

We can see that the vertex of the parabola is at point (2,1). This means that ℎ=2 and 𝑘=1.

Next, we can choose another point on the parabola, for example (0,-3) or (4,-3), and substitute these values into the equation 𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘 to solve for 𝑎.

Using (0,-3), we have:

-3 = 𝑎(0 − 2)2 + 1

-3 = 4𝑎 + 1

-4 = 4𝑎

𝑎 = -1

Therefore, the equation of the parabola is:

𝑦 = -1(𝑥 − 2)2 + 1

or

𝑦 = -(𝑥^2 - 4𝑥 + 4) + 1

or

𝑦 = -𝑥^2 + 4𝑥 - 3