PLS HELP!!! Note: Enter your answer and all the steps that you use to solve this problem in the space provided below. Write the equation in vertex form: y=x^2+2x+5

Question

PLS HELP!!! algebra 2 vertexes

Answer 1

You will need to know how to complete the square to convert to vertex form.

y = (x² + 2x + ___) + 5 [since the leading coefficient is 1, simply group the 1st two terms leaving a space to "complete the square", which converts the expression in parentheses to a perfect square trinomial]

To complete the square, take half of b and square it. Since b = 2, 1/2 (2) = 1 and 1²=1. You are going to place a 1 in the placeholder so you need to subtract 1 to compensate:

y = (x² + 2x + 1) + 5 - 1

y = (x² + 2x + 1) + 4

Now rewrite the trinomial as a binomial squared.

y = (x + 1)² + 4

In that form it is easy to identify the vertex as (-1, 4).

The following Desmos graph shows the parabola in both forms along with the vertex.

Rows 4 -12 generalize the process for converting from standard form to vertex form.

desmos.com/calculator/vfulna0ai9

Use the sliders on a,b,c to see the generalized parabola take on different forms.

Rows 13-17 show a more complicated example for converting from standard to vertex form.