Use the completeing the square method to find the vertex from the quadratic function y=x^2+5x+12?

Answer 1

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Answer 2

y = x^2 + 5x + 12

I'm going to add 25/4 and subtract 25/4

y = x^2 + 5x + 25/4 + 12 - 25/4

Now, the first three terms form a perfect square binomial.

y = (x + 5/2)^2 + 12 - 25/4

Let's clean up the two numbers at the tail end, shall we?

y = (x + 5/2)^2 + 48/4 - 25/4
y = (x + 5/2)^2 + 23/4

The vertex form of a quadratic function goes as follows:

y = a(x - h) + k, where (h, k) is the vertex.

For that reason, to get h, we take the NEGATIVE of 5/2.

Our vertex is at (-5/2, 23/4)

Answer 3

X^2 + 5x + ( ) = 12 + ( )
X^2 + 5x + 6.25 = 12 + 6.25
(X + 2.5)^2 = 18.25
X+2.5 = +or- root(18.25)
X = -2.5 +or- root(18.25)

Since -2.5 would be in-between the two places where x=0, plug it into the equation and see what y equals.

(-2.5)^2 + 5(-2.5) + 12
6.25 - 12.5 + 12 = 6.25 - .5 = 5.75

So the vertex would be at (-2.5 , 5.75)