What are the vertex and focus of the parabola with equation y=x2+8x+10?
Identify the vertex.
To find the vertex and focus of the parabola with equation y=x^2+8x+10, we first need to rewrite the equation in vertex form:
y = (x+4)^2 - 6
Now we can see that the vertex of the parabola is at (-4, -6).
To find the focus of the parabola, we can use the formula for a parabola opening upwards: (h, k + p), where p is the distance from the vertex to the focus.
In this case, p = 1/4. So the focus of the parabola is at (-4, -23/4).