SOLUTION: y=x^2-2x-1 graph the quadratic function. label the vertex and axis of semitry.

Question 176546This question is from textbook algebra 2
: y=x^2-2x-1 graph the quadratic function. label the vertex and axis of semitry. This question is from textbook algebra 2

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Table of Contents:
Step 1: Finding the Vertex
Step 2: Finding two points to left of axis of symmetry
Step 3: Reflecting two points to get points right of axis of symmetry
Step 4: Plotting the Points (with table)
Step 5: Graphing the Parabola

In order to graph , we can follow the steps:

Step 1) Find the vertex (the vertex is the either the highest or lowest point on the graph). Also, the vertex is at the axis of symmetry of the parabola (ie it divides it in two).

Step 2) Once you have the vertex, find two points on the left side of the axis of symmetry (the line that vertically runs through the vertex).

Step 3) Reflect those two points over the axis of symmetry to get two more points on the right side of the axis of symmetry.

Step 4) Plot all of the points found (including the vertex).

Step 5) Draw a curve through all of the points to graph the parabola.

Let's go through these steps in detail

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Step 1)

Finding the vertex:

In order to find the vertex, we first need to find the x-coordinate of the vertex.

To find the x-coordinate of the vertex, use this formula: .

Start with the given formula.

From , we can see that , , and .

Plug in and .

Negate to get .

Multiply 2 and to get .

Divide.

So the x-coordinate of the vertex is . Note: this means that the axis of symmetry is also .

Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.

Start with the given equation.

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So the y-coordinate of the vertex is .

So the vertex is

.

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Step 2)

Find two points to the left of the axis of symmetry:

Let's find the y value when

Start with the given equation.

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So the first point to the left of the axis of symmetry is (-1,2)

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Let's find the y value when

Start with the given equation.

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So the second point to the left of the axis of symmetry is (0,-1)

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Step 3)

Reflecting the two points over the axis of symmetry:

Now remember, the parabola is symmetrical about the axis of symmetry (which is )

This means the y-value for (which is one unit from the axis of symmetry) is equal to the y-value of (which is also one unit from the axis of symmetry). So when , which gives us the point (2,-1). So we essentially reflected the point (0,-1) over to (2,-1).

Also, the y-value for (which is two units from the axis of symmetry) is equal to the y-value of (which is also two units from the axis of symmetry). So when , which gives us the point (3,2). So we essentially reflected the point (-1,2) over to (3,2).

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Step 4)

Plotting the points:

Now lets make a table of the values we have calculated:

x	y
-1	2
0	-1
1	-2
2	-1
3	2

Now let's plot the points:

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Step 5)

Drawing a curve through all of the points:

Now draw a curve through all of the points to graph :

Graph of
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