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
Given the following graph of a parabola, find its equation, in the form
𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘
1 answer