SOLUTION: What does it mean to find the vertex, intercepts, and sketch of y=-x2-6x+1?

Question 147564: What does it mean to find the vertex, intercepts, and sketch of y=-x2-6x+1?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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 .

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

Intercepts:

Y-intercept:

To find the y-intercept, simply plug in and simplify.

Start with the given equation.

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , . This means that the y-intercept is (0,1).

------------------

X-intercept:

To find the x-intercept, simply plug in and solve for x.

Start with the given equation.

Plug in

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

Break up the fraction.

Reduce.

or Break up the expression.

So our answers are or

which approximate to or

So the x-intercepts are roughly

and

With all of this info, we can now sketch the graph:

Graph of

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