What is the vertex of y=−3x2−5x−(3x−2)2?

2 Answers
turksvids
Dec 30, 2017

The vertex is (724,−14348).

Explanation:

First expand (3x−2)2=9x2−12x+4.

Substituting that in we have:

y=−3x2−5x−(9x2−12x+4)

Distribute the negative:

y=−3x2−5x−9x2+12x−4

Collect like terms:

y=−12x2+7x−4

The vertex is (h,k) where h=−b2a and k is the value of y when h is substituted.

h=−72(−12)=724.

k=−12(724)2+7(724)−4=−14348 (I used a calculator...)

The vertex is (724,−14348).

Jim G.
Dec 30, 2017

(724,−14348)

Explanation:

we require to express in standard form

⇒y=−3x2−5x−(9x2−12x+4)

⇒y=−3x2−5x−9x2+12x−4

⇒y=−12x2+7x−4←in standard form

given the equation of a parabola in standard form then
the x-coordinate of the vertex is

xvertex=−b2a

here a=−12,b=7,c=−4

⇒xvertex=−7−24=724

substitute this value into the equation for y

y=−12(724)2+7(724)−4=−14348

⇒vertex =(724,−14348)

Related questions
See all questions in Quadratic Functions and Their Graphs
Impact of this question
2142 views around the world
You can reuse this answer
Creative Commons License