What is the vertex of y= -2(x - 4)^2 - 5x+3 y=−2(x−4)2−5x+3?

1 Answer
Joel R.
Jan 6, 2016

The vertex is (11/4, -111/8)(114,−1118)

Explanation:

One of the forms of the equation of a parabola is y = a(x-h)^2 + ky=a(x−h)2+k where (h, k) is the vertex. We can transform the above equation into this format to determine the vertex.

Simplify
y = -2(x^2 - 8x +16) - 5x + 3y=−2(x2−8x+16)−5x+3

It becomes
y = -2x^2+16x-32-5x+3y=−2x2+16x−32−5x+3
y = -2x^2+11x-29y=−2x2+11x−29

Factor out 2 being the coefficient of x^2x2
y = -2(x^2-11/2x+29/2)y=−2(x2−112x+292)

Complete the square: Divide by 2 the coefficient of x and then square the result. The resulting value becomes the constant of the perfect square trinomial.

((-11/2)/2)^2 = 121/16(−1122)2=12116

We need to add 121/16 to form a perfect square trinomial. We have to deduct it as well though, to preserve the equality. The equation now becomes

y = -2(x^2-11/2x+ 121/16 -121/16 +29/2)y=−2(x2−112x+12116−12116+292)

Isolate the terms which form the perfect square trinomial

y = -2(x^2-11/2x+ 121/16) +121/8 -29y=−2(x2−112x+12116)+1218−29
y = -2(x^2-11/2x+ 121/16) -111/8y=−2(x2−112x+12116)−1118
y = -2(x^2-11/4)^2 -111/8y=−2(x2−114)2−1118

From this
h = 11/4h=114
k = -111/8k=−1118
Hence, the vertex is (11/4, -111/8)(114,−1118)

Related questions
See all questions in Quadratic Functions and Their Graphs
Impact of this question
1532 views around the world
You can reuse this answer
Creative Commons License