13. For the following graph of the parabola, find its equation in the form
𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘. Then, express the answer in standard or expanded form,
𝑦 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐.
It is not possible to provide an answer without the graph of the parabola. Please provide the graph.
To find the equation of the parabola in the form 𝑦 = 𝑎(𝑥 − ℎ)² + 𝑘, we need to determine the values of 𝑎, ℎ, and 𝑘.
1. Determine the vertex of the parabola: The vertex is the point on the parabola where it reaches its minimum or maximum value. In the given graph, the vertex appears to be at the point (𝐻, 𝐾), where ℎ represents the horizontal shift and 𝑘 represents the vertical shift.
2. Determine the value of 𝑎: The value of 𝑎 determines the steepness or the width of the parabola. If 𝑎 > 0, the parabola opens upward, and if 𝑎 < 0, the parabola opens downward. To find the value of 𝑎, we need to examine the graph and the vertex.
3. Rewrite the equation in standard or expanded form: Once we have the values of 𝑎, ℎ, and 𝑘, we can rewrite the equation in the form 𝑦 = 𝑎𝑥² + 𝑏𝑥 + 𝑐, where 𝑏 and 𝑐 are constants.
Without the specific details of the graph or coordinates, it is not possible to provide the exact equation of the parabola. However, by following these steps, you should be able to determine the equation of the parabola based on the given information.