Graph y=(x+1)^2-7

Math
y=(x+1)2-7
Find the properties of the given parabola.
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Use the vertex form, y=a(x-h)2+k, to determine the values of a, h, and k.
a=1
h=-1
k=-7
Since the value of a is positive, the parabola opens up.
Opens Up
Find the vertex (h,k).
(-1,-7)
Find p, the distance from the vertex to the focus.
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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.
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Cancel the common factor.
14⋅1
Rewrite the expression.
14
14
14
Find the focus.
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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,-274)
(-1,-274)
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
x=-1
Find the directrix.
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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=-294
y=-294
Use the properties of the parabola to analyze and graph the parabola.
Direction: Opens Up
Vertex: (-1,-7)
Focus: (-1,-274)
Axis of Symmetry: x=-1
Directrix: y=-294
Direction: Opens Up
Vertex: (-1,-7)
Focus: (-1,-274)
Axis of Symmetry: x=-1
Directrix: y=-294
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.
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Replace the variable x with -2 in the expression.
f(-2)=(-2)2+2(-2)-6
Simplify the result.
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Simplify each term.
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Raise -2 to the power of 2.
f(-2)=4+2(-2)-6
Multiply 2 by -2.
f(-2)=4-4-6
f(-2)=4-4-6
Simplify by subtracting numbers.
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Subtract 4 from 4.
f(-2)=0-6
Subtract 6 from 0.
f(-2)=-6
f(-2)=-6
The final answer is -6.
-6
-6
The y value at x=-2 is -6.
y=-6
Replace the variable x with -3 in the expression.
f(-3)=(-3)2+2(-3)-6
Simplify the result.
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Simplify each term.
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Raise -3 to the power of 2.
f(-3)=9+2(-3)-6
Multiply 2 by -3.
f(-3)=9-6-6
f(-3)=9-6-6
Simplify by subtracting numbers.
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Subtract 6 from 9.
f(-3)=3-6
Subtract 6 from 3.
f(-3)=-3
f(-3)=-3
The final answer is -3.
-3
-3
The y value at x=-3 is -3.
y=-3
Replace the variable x with 0 in the expression.
f(0)=(0)2+2(0)-6
Simplify the result.
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Simplify each term.
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Raising 0 to any positive power yields 0.
f(0)=0+2(0)-6
Multiply 2 by 0.
f(0)=0+0-6
f(0)=0+0-6
Simplify by adding zeros.
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Add 0 and 0.
f(0)=0-6
Subtract 6 from 0.
f(0)=-6
f(0)=-6
The final answer is -6.
-6
-6
The y value at x=0 is -6.
y=-6
Replace the variable x with 1 in the expression.
f(1)=(1)2+2(1)-6
Simplify the result.
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Simplify each term.
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One to any power is one.
f(1)=1+2(1)-6
Multiply 2 by 1.
f(1)=1+2-6
f(1)=1+2-6
Simplify by adding and subtracting.
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Add 1 and 2.
f(1)=3-6
Subtract 6 from 3.
f(1)=-3
f(1)=-3
The final answer is -3.
-3
-3
The y value at x=1 is -3.
y=-3
Graph the parabola using its properties and the selected points.
xy-3-3-2-6-1-70-61-3
xy-3-3-2-6-1-70-61-3
Graph the parabola using its properties and the selected points.
Direction: Opens Up
Vertex: (-1,-7)
Focus: (-1,-274)
Axis of Symmetry: x=-1
Directrix: y=-294
xy-3-3-2-6-1-70-61-3
Graph y=(x+1)^2-7

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