How do you write # y=x^2+2x-35# in vertex form?

Question

Eva Adamson · Accepted Answer

see below

#y = x^2 + 2x -35# use completing a square, #y = (x + 1)^2 - (1)^2 - 35# #y = (x + 1)^2 - 36# since #(x + 1)^2# has a +ve value, it is a minimum vertex #-35# at #(-1, -35)#

Jameson Allen · Answer

undefined To write the quadratic function $ y = x^2 + 2x - 35 $ in vertex form, you can complete the square. The vertex form of a quadratic function is given by $ y = a(x - h)^2 + k $, where $(h, k)$ represents the vertex of the parabola. To complete the square, follow these steps:

1. Group the $ x^2 $ and $ x $ terms together.
2. Factor out the coefficient of $ x^2 $ from $ x^2 + 2x $.
3. Complete the square by adding and subtracting $(\frac{b}{2})^2$, where $b$ is the coefficient of the linear term.
4. Rewrite the expression as a perfect square trinomial.
5. Adjust the constant term if needed.

Following these steps:

1. Group the terms: $ y = (x^2 + 2x) - 35 $
2. Factor out the coefficient of $ x^2 $: $ y = (x^2 + 2x + 1 - 1) - 35 $
3. Complete the square: $ y = (x^2 + 2x + 1) - 1 - 35 $
4. Rewrite as a perfect square trinomial: $ y = (x + 1)^2 - 36 $

Therefore, the quadratic function $ y = x^2 + 2x - 35 $ in vertex form is $ y = (x + 1)^2 - 36 $.