What is the the vertex of y=3x2+4x−18?

2 Answers
Tony B
Feb 26, 2016

xvertex=−23 I will let the reader find yvertex

Explanation:

Given: y=3x2+4x−18 ..................................(1)

Write as: y=3(x2+43x)−18

Using the +43 from (x2+43x)

(−12)×43=−46=−23

xvertex=−23

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
−23 = −0.6666¯6 = −0.6667 to 4 decimal places

All you have to do now is substitute x=−23 intoequation (1) to find yvertex

Tony BTony B

P dilip_k
Feb 26, 2016

May be done as follows

Explanation:

The given equation is
y=3x2+4x−18
⇒y=3[x2+2x(23)+(23)2−(23)2−6]

⇒y=3[(x+23)2−(23)2−6]
⇒y=3[(x+23)2−49−6]
⇒y=3[(x+23)2−589]
⇒y=3(x+23)2−589⋅3
⇒y+583=3(x+23)2
putting ,y+583=Yandx+23=X we have
new equation
Y=3X2,which has coordinate of vertex (0,0)
So putting X=0 and Y=0 in the above relation
we get
x=−23
and y=−583=−1913

so the actual coordinate of vertex is (−23,−1913)

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