Question

Find the vertex of each parabola. $$y=-2 x^{2}+12 x-17$$

   Find the vertex of each parabola.
$$y=-2 x^{2}+12 x-17$$

College Algebra

College Algebra

R. David Gustafson,… 11th Edition

Chapter 3, Problem 27

Instant Answer

Solved by Expert James Kiss

07/07/2020

Step 1

The quadratic equation is in the form of \(y = ax^2 + bx + c\). Comparing this with the given equation \(y = -2x^2 + 12x - 17\), we get \(a = -2\), \(b = 12\), and \(c = -17\). Show more…

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Find the vertex of each parabola. $$y=-2 x^{2}+12 x-17$$

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Key Concepts

Completing the Square

Completing the square is a method used to transform a quadratic expression from its standard form into vertex form. This technique involves creating a perfect square trinomial, which not only simplifies the expression but also directly reveals the vertex of the parabola.

Quadratic Function

A quadratic function is a type of polynomial function defined by the equation y = ax² + bx + c, where a, b, and c are constants. It graphs as a parabola, opening upward when the coefficient a is positive and downward when a is negative.

Vertex of a Parabola

The vertex of a parabola is its turning point, representing either the maximum or minimum value of the quadratic function. It can be located using the formula x = -b/(2a) for the horizontal coordinate, with the corresponding y-value found by substituting that x-value back into the equation.

Standard Form and Vertex Form

Quadratic functions can be expressed in standard form (y = ax² + bx + c) or vertex form (y = a(x-h)² + k), where (h, k) is the vertex. Converting from standard form to vertex form, often through completing the square, makes it straightforward to identify the vertex and other properties of the parabola.

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