Question

Make a t-table of values for y = x2 + 4x + 1. A suggestion is to begin your values with -5.

1.List your ordered pairs from the table. Use parenthesis for each pair, such as (-1,2).

2.Which point is the vertex of the parabola?

a) (-2, -3)
b) (2, 3)
c) (-2, 3)
d) (2, -3)

3. The line which you folded is called the line of symmetry. This divides the parabola into two matching halves or mirror images. The equation of the line is x = ___ because it is vertical. Look to see where your folded line crosses the x-axis. Choose the equation below.

a) x = -2
b) x = 2
c) x = 0
d)None

Answer 1

You can write a table on your own.

On to the vertex;
When an equation is written as:
\[f(x)=ax^2+bx+c\]
The vertex of a parabola will be the point:
\[(-\frac{b}{2a},f(-\frac{b}{2a}))\]
\[Vertex (-\frac{4}{2(1)},f(-\frac{4}{2(1)}))=(-2, f(-2))=(-2,-3)\]

To find the line of symmetry, you can rewrite the equation to this form and the line of symmetry will be at x=h:
\[f(x)=a(x-h)^2+K\]
To do this, you need to complete the square for x.
\[ y = x^2 + 4x + 1\]
\[y=1(x^2+4x+4-4+1)=(x+2)^2-3\]
From this we can see that h=-2.
The line of symmetry is at x=h=-2.