4. Given the following graph of a parabola, find its equation, in the form
𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘
Without a graph provided, we cannot find the equation of the parabola. We would need at least three points on the parabola to determine its equation.
To find the equation of the given parabola, we need to identify the vertex and the value of 'a'.
The vertex of a parabola in the form 𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘 is given by the coordinates (h, k).
Looking at the graph, we can see that the vertex of the parabola is at the point (2, -3).
Now, let's identify the value of 'a'. To do this, we can look at the direction the parabola opens. If it opens upwards, 'a' is positive, and if it opens downwards, 'a' is negative.
From the graph, it is clear that the parabola opens upwards. Therefore, 'a' is positive.
Now we have the vertex (h, k) = (2, -3) and 'a' is positive. We can substitute these values into the equation 𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘 to get the equation of the parabola.
Substituting h = 2, k = -3, and a = positive value, the equation of the parabola is 𝑦 = 𝑎(𝑥 − 2)2 - 3.