13. Graph the following quadratic functions identifying and labeling thecoordinates of the intercepts, the vertex and the axis of symmetry1)2) y = -2x2 – 5x + 1|

Answered: 13. Graph the following quadratic…

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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Question

13. Graph the following quadratic functions identifying and labeling the
coordinates of the intercepts, the vertex and the axis of symmetry
1)
2) y = -2x2 – 5x + 1
|

Expert Solution

Step 1

$y = - 2 x^{2} - 5 x + 1$

first we find out the x intercept

Replace y with 0 and solve for x

$0 = - 2 x^{2} - 5 x + 1 A p p l y q u a d r a t i c f o r m u l a x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} x = \frac{5 \pm \sqrt{{(- 5)}^{2} - 4 (- 2) (1)}}{2 (- 2)} x = \frac{- 5 \pm \sqrt{33}}{4} x i n t e r c e p t s (\frac{- 5 - \sqrt{33}}{4}, 0) a n d (\frac{- 5 - \sqrt{33}}{4}, 0)$

Step 2

To find out y intercept we plug in 0 for x

$y = - 2 x^{2} - 5 x + 1 y = - 2 {(0)}^{2} - 5 (0) + 1 y = 1 y i n t e r c e p t (0, 1)$

find out vertex using formula

$x = \frac{- b}{2 a} x = \frac{- (- 5)}{2 (- 2)} = \frac{- 5}{4} S u b s t i t u t e x a n d f i n d o u t y y = - 2 x^{2} - 5 x + 1 y = - 2 {(\frac{- 5}{4})}^{2} - 5 (\frac{- 5}{4}) + 1 = \frac{33}{8} v e r t e x (\frac{- 5}{4}, \frac{33}{8})$

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