1) Find the vertex of each parabola. 2) Use the discriminant to determine the number of x-intercepts the graph will have. Then determine the x-intercepts. The image contains the following mathematical expression, which appears to be an algebraic function:**17. $ G(x) = -2x^2 + 4x - 5 $**This is a quadratic function described by the equation $ G(x) = -2x^2 + 4x - 5 $. It represents a parabola that opens downward due to the negative coefficient of the $ x^2 $ term. The function can also be analyzed to find specific characteristics such as its vertex, axis of symmetry, and roots by applying algebraic methods such as completing the square or using the quadratic formula.

Answered: 17. G(x) = - 2x² + 4x – 5 %3D

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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1) Find the vertex of each parabola. 2) Use the discriminant to determine the number of x-intercepts the graph will have. Then determine the x-intercepts.

The image contains the following mathematical expression, which appears to be an algebraic function:

**17. $ G(x) = -2x^2 + 4x - 5 $**

This is a quadratic function described by the equation $ G(x) = -2x^2 + 4x - 5 $. It represents a parabola that opens downward due to the negative coefficient of the $ x^2 $ term. The function can also be analyzed to find specific characteristics such as its vertex, axis of symmetry, and roots by applying algebraic methods such as completing the square or using the quadratic formula.

Expert Solution

Step 1

GIVEN DATA : Equation of Parabola $G (x) = - 2 x^{2} + 4 x - 5$

TO FIND : Vertex of $G (x)$ , Number of $X -$ intercepts, and the $X -$ intercepts of the parabola

(1). The Vertex of Parabola in the form of $y = a x^{2} + b x + c$ is $x = \frac{- b}{2 a}$

Compare the given parabola Equation $G (x) = - 2 x^{2} + 4 x - 5$ and evaluate the $a, b & c$

$a = (- 2)$ , $b = 4$ and $c = (- 5)$

Thus, vertex will be

$x = \frac{- b}{2 a}$

$x = \frac{- 4}{2 (- 2)}$

$x = 1$

Plug the value of $x = 1$ in the equation of parabola to

$y = - 2 x^{2} + 4 x - 5$

$y = - 2 {(1)}^{2} + 4 (1) - 5$

$y = - 2 + 4 - 5$

$y = (- 3)$

Thus, Vertex of the $G (x) = - 2 x^{2} + 4 x - 5$ is $(1, - 3)$

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