can you explain in detail how to get the answers # Analyzing a Parabola: Vertex, Focus, and DirectrixWhen given the equation of a parabola, it is often useful to find its vertex, focus, and directrix to better understand its shape and position on a graph. Consider the equation:\[(x - 6)^2 = 2(y + 4)\]## Key Components### VertexThe vertex of the parabola is a key point where the curve changes direction. For the equation given, the vertex is located at:\[(x, y) = (6, -4)\]### FocusThe focus is a point inside the parabola where all the reflected lines (from a point on the parabola) converge. The focus here is:\[(x, y) = (6, -3.5)\]### DirectrixThe directrix is a line perpendicular to the axis of symmetry of the parabola, providing a reference for measuring distances to any point on the parabola. For this parabola:\[y = -4.5\]## Graphical Representation- **First Graph (bottom-left):** This graph correctly represents the parabola. It opens upwards, and the vertex is located at (6, -4) with symmetry along the vertical axis. The scale and orientation match our vertex, focus, and directrix.- **Second Graph (top-left):** This graph incorrectly depicts a parabola opening upwards with a vertex not matching (6, -4).- **Third Graph (top-middle):** This graph depicts a downward-opening parabola, which contradicts the calculated parameters since the vertex is at (6, -4), and the parabola should open upwards.- **Fourth Graph (top-right):** Similarly, this graph also incorrectly shows a downward-opening parabola.Upon examining these graphs, the correct graph (bottom-left) demonstrates the parabola correctly according to the given equation parameters.

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Find the vertex, focus, and directrix of the parabola, and sketch its graph. (x - 6)2 = 2(y + 4) = 0 (x,y) = 6,-4 (x, y) = 6,- 3.5 y = - 4.5 vertex focus directrix hin با 15r 10 5 5 5 -15L مجار 10 5 15 10 15 X X y 15 10 5 5 10 15 -5 -10 -15 5 10 15 X

Find the vertex, focus, and directrix of the parabola, and sketch its graph. (x - 6)2 = 2(y + 4) = 0 (x,y) = 6,-4 (x, y) = 6,- 3.5 y = - 4.5 vertex focus directrix hin با 15r 10 5 5 5 -15L مجار 10 5 15 10 15 X X y 15 10 5 5 10 15 -5 -10 -15 5 10 15 X

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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