You are here:

- Home
- Science
- Math for Kids
- Algebra
- Find the vertex (Algebra II)

Advertisement

Find the Vertex of (x-3)2+5?

Solve by completing the square:

x2+2x-15 = 0?

and

Write the Quadratic function in Vertex Form:

x2+4x+5?

I take it the 2 at the end is really for a square, as in (x-3)2 is (x-3)².

If y = (x-3)² + 5, the minimum is found at x=3, and that is the vertex.

Putting in x=3 makes the value in the parenthesis 0, so that answer is y=5.

This makes the vertex at the point (3,5).

For x²+2x-15, the first thing to look at is the factors of 15.

Since 15 = 3*5, the numbers to try are 3 and 5.

Since -15 is negative, one of them needs to be negative.

Since the +2 is positive, the larger of the two needs to be positive.

This means to try (x+5)(x-3).

This gives x² + 5x - 3x -15.

Combining the x terms gives x² + 2x - 15, and that's what we're looking for.

Writing x² + 4x + 5 in quadratic form means writing it as (x+a)² + b.

To find a, note that it is half the x factor.

Since the x factor is 4, that makes a 2.

Since we have (x+2)², that works out to x² + 2x + 4.

Now that 4 added on must be subtracted from the 5 we have already, and 5-4=1.

This gives (x+2)² + 1.

The vertex can then be seen to be (-2,1).

Algebra

Answers by Expert:

Any algebraic question you've got. That includes question that are linear, quadratic, exponential, etc.

I have solved story problems, linear equations, parabolic equations.
I have also solved some 3rd order equations and equations with multiple variables.
**Publications**

Documents at Boeing in assistance on the manufacturiing floor.**Education/Credentials**

MS at math OSU in mathematics at OSU, 1986.
BS at OSU in mathematical sciences (math, statistics, computer science), 1984.
**Awards and Honors**

Both my BS and MS degrees were given with honors.
**Past/Present Clients**

Students in a wide variety of areas since the 80's; over 1,000 of them have been in algebra.