### Writing Equations from Quadratic Graphs**Task:** Write an equation (any form) for the quadratic graphed below:**Graph Details:**- The graph depicts a quadratic function, showing a parabolic curve opening downwards.- The vertex of the parabola is at the point (2, 2).- The parabola intersects the x-axis at approximately (0,0) and (4,0).- The y-axis ranges from -5 to 5.- The x-axis ranges from -5 to 5.**How to Determine the Equation:**1. **Identify Key Features:** - Vertex (h, k): (2, 2) - X-intercepts: (0, 0) and (4, 0)2. **Using Vertex Form of a Quadratic Function:** The vertex form of a quadratic equation is given by: \[ y = a(x - h)^2 + k \] Substituting the vertex (2, 2): \[ y = a(x - 2)^2 + 2 \]3. **Determine 'a' Using Another Point:** Use one of the x-intercepts, say (0, 0), to find the value of 'a'. \[ 0 = a(0 - 2)^2 + 2 \] \[ 0 = 4a + 2 \] \[ -2 = 4a \] \[ a = -\frac{1}{2} \]4. **Write the Final Equation:** \[ y = -\frac{1}{2}(x - 2)^2 + 2 \]**Conclusion:**The equation of the quadratic graph is:\[y = -\frac{1}{2}(x - 2)^2 + 2\]Please enter the equation in the box provided:```y = [ ]```

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Answered: Write an equation (any form) for the…

Math

Algebra

Write an equation (any form) for the quadratic graphed below: -5 -4 -3 -2 -1 5 S ON 2 T 7 -2 -3 -4 5 -N 4 5 a

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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