How do you find the vertex and intercepts for y=2x2+3x−8?

1 Answer
Nallasivam V
May 30, 2018

Vertex (−34,−738)
Y-Intercept (0,−8)
x-intercept (√73−34,0);(−√73−34,0)

Explanation:

Given -

y=2x2+3x−8

x=−b2a=−32×2=−34=−34

At x=−34;y=2(−34)2+3(−34)−8

y=2(−916)−94−8

y=1816−94−8=18−36−12816=−14616=−738

Vertex

(−34,−738)

Intercept

Y-Intercept

At x=0;y=2(02)+3(0)−8=−8

(0,−8)

X-intercept

At y=0;0=2x2+3x−8

2x2+3x−8=0

2x2+3x=8

x2+32x=4

x2+32x+916=4+916=64+916=7316

(x+34)2=±√7316

x+34=±√7316=±√734

x=√734−34=√73−34

x=−√734−34=−√73−34

x-intercept (√73−34,0);(−√73−34,0)

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