Question

sketch the graph of the given equation. $y^2+6 y+9=0$

   sketch the graph of the given equation.
$y^2+6 y+9=0$

Modern Analytic Geometry

Modern Analytic Geometry

William Wooton,… 1st Edition

Chapter 5, Problem 35

Instant Answer

Solved by Expert Ankit Gupta

07/24/2020

Step 1

This is a quadratic equation in the standard form \( ay^2 + by + c = 0 \), where \( a = 1 \), \( b = 6 \), and \( c = 9 \). Show more…

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sketch the graph of the given equation. $y^2+6 y+9=0$

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Key Concepts

Perfect Square Trinomial

A perfect square trinomial is an expression that can be factored into the square of a binomial. Recognizing the form a² + 2ab + b² as (a + b)² helps simplify and solve quadratic equations.

Solving Quadratic Equations

This involves setting a quadratic expression equal to zero and finding the value or values of the variable that satisfy the equation. In cases where the quadratic factors into a perfect square, the solution is a repeated root.

Graphing Horizontal Lines

Graphing horizontal lines involves plotting all points in the plane that have the same y-coordinate. When a quadratic equation simplifies to a constant value for y, the graph represents a horizontal line at that y-value.

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