# Graph y+2=(x+1)^2 y+2=(x+1)2
Find the properties of the given parabola.
Subtract 2 from both sides of the equation.
y=(x+1)2-2
Use the vertex form, y=a(x-h)2+k, to determine the values of a, h, and k.
a=1
h=-1
k=-2
Since the value of a is positive, the parabola opens up.
Opens Up
Find the vertex (h,k).
(-1,-2)
Find p, the distance from the vertex to the focus.
Find the distance from the vertex to a focus of the parabola by using the following formula.
14a
Substitute the value of a into the formula.
14⋅1
Cancel the common factor of 1.
Cancel the common factor.
14⋅1
Rewrite the expression.
14
14
14
Find the focus.
The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down.
(h,k+p)
Substitute the known values of h, p, and k into the formula and simplify.
(-1,-74)
(-1,-74)
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
x=-1
Find the directrix.
The directrix of a parabola is the horizontal line found by subtracting p from the y-coordinate k of the vertex if the parabola opens up or down.
y=k-p
Substitute the known values of p and k into the formula and simplify.
y=-94
y=-94
Use the properties of the parabola to analyze and graph the parabola.
Direction: Opens Up
Vertex: (-1,-2)
Focus: (-1,-74)
Axis of Symmetry: x=-1
Directrix: y=-94
Direction: Opens Up
Vertex: (-1,-2)
Focus: (-1,-74)
Axis of Symmetry: x=-1
Directrix: y=-94
Select a few x values, and plug them into the equation to find the corresponding y values. The x values should be selected around the vertex.
Replace the variable x with -2 in the expression.
f(-2)=(-2)2+2(-2)-1
Simplify the result.
Simplify each term.
Raise -2 to the power of 2.
f(-2)=4+2(-2)-1
Multiply 2 by -2.
f(-2)=4-4-1
f(-2)=4-4-1
Simplify by subtracting numbers.
Subtract 4 from 4.
f(-2)=0-1
Subtract 1 from 0.
f(-2)=-1
f(-2)=-1
The final answer is -1.
-1
-1
The y value at x=-2 is -1.
y=-1
Replace the variable x with -3 in the expression.
f(-3)=(-3)2+2(-3)-1
Simplify the result.
Simplify each term.
Raise -3 to the power of 2.
f(-3)=9+2(-3)-1
Multiply 2 by -3.
f(-3)=9-6-1
f(-3)=9-6-1
Simplify by subtracting numbers.
Subtract 6 from 9.
f(-3)=3-1
Subtract 1 from 3.
f(-3)=2
f(-3)=2
The final answer is 2.
2
2
The y value at x=-3 is 2.
y=2
Replace the variable x with 0 in the expression.
f(0)=(0)2+2(0)-1
Simplify the result.
Simplify each term.
Raising 0 to any positive power yields 0.
f(0)=0+2(0)-1
Multiply 2 by 0.
f(0)=0+0-1
f(0)=0+0-1
Simplify by adding zeros.
Add 0 and 0.
f(0)=0-1
Subtract 1 from 0.
f(0)=-1
f(0)=-1
The final answer is -1.
-1
-1
The y value at x=0 is -1.
y=-1
Replace the variable x with 1 in the expression.
f(1)=(1)2+2(1)-1
Simplify the result.
Simplify each term.
One to any power is one.
f(1)=1+2(1)-1
Multiply 2 by 1.
f(1)=1+2-1
f(1)=1+2-1
Simplify by adding and subtracting.
Add 1 and 2.
f(1)=3-1
Subtract 1 from 3.
f(1)=2
f(1)=2
The final answer is 2.
2
2
The y value at x=1 is 2.
y=2
Graph the parabola using its properties and the selected points.
xy-32-2-1-1-20-112
xy-32-2-1-1-20-112
Graph the parabola using its properties and the selected points.
Direction: Opens Up
Vertex: (-1,-2)
Focus: (-1,-74)
Axis of Symmetry: x=-1
Directrix: y=-94
xy-32-2-1-1-20-112
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