Question

The equation of a parabola is y=x2+6x+9. Write the equation in vertex form.

Answer 1

Answer:

Step-by-step explanation:

Vertex form is accomplished by completing the square on the quadratic. Do this by first setting the parabola equal to 0 then moving the constant over to the other side:

$x^2+6x=-9$

Now take half the linear term, square it, and add it to both sides. Our linear term is 6. Half of 6 is 3, and 3 squared is 9:

$x^2+6x+9=-9+9$

The reason we do this is to create a perfect square binomial on the left:

$(x+3)^2=0$ (obviously the 0 results from the addition of 9 and -9). Move the 0 back over to the other side and set the quadratic back equal to y:

$(x+3)^2+0=y$

This gives you a vertex of (-3, 0), which is a minimum value, since the parabola opens upwards.