Finding the Vertex Using the X-intercepts

Presentation

•

Mathematics

•

9th - 12th Grade

•

Medium

•

CCSS

HSF-IF.C.7A, HSG.GPE.A.2, HSA.APR.B.3

Standards-aligned

Marcie Borchard

Used 4+ times

FREE Resource

14 Slides • 20 Questions

Finding the Vertex from Roots

You now know how to find the x-intercepts from factoring. Now we will use the x-intercepts to find the vertex.

We know that the shape of a parabola is symetrical. What divides the parabola? The axis of symmetry.

Finding the Axis of Symmetry

Line of Symmetry.

It is a line so it will always look like x = #.

Multiple Choice

The line that goes through the middle of a parabola is called the...

Vertex

Axis of Symmetry

x-intercept

y-intercept

Multiple Choice

What is the green dashed line called?

roots or x-intercepts

parabola

axis of symmetry

line of dashes

Did you notice that the axis of symmetry went through the vertex?

Multiple Choice

What is the equation for axis of symmetry?

y=3

x=3

x=5

x=1

The axis of symmetry was x = 3.

We will use that 3 as the x value in our VERTEX!

Multiple Choice

What is the vertex of this parabola?

(0, 5)

(0, 0)

(-4, 5)

(-2, 1)

Multiple Choice

What is the axis of symmetry?

y = 5

y = 1

-2

x = -2

Multiple Choice

What is the vertex?

(4,-4)

(2,0)

(0,2)

(6,0)

Multiple Choice

What is the axis of symmetry?

x = 4

x = 2

x = 6

(4, -6)

Finding the axis of symmetry from the x-intercepts.

If you noticed from the last slide, the x-intercepts were 2 and 6, the axis of symmetry was x = 4. Do you see how the intercepts are related to the axis of symmetry? What is between 2 and 6? 4!

If you can find the x-intercepts you can find the axis of symmetry.

Find the average of the x-intercepts by adding them together and dividing them by 2.
Example

\frac{\left(2+6\right)}{2}\ =\ \frac{8}{2}\ =\ 4

The axis of symmetry is x = 4

Multiple Select

What are the x-intercepts?

-3

7 1/2

Multiple Choice

What is the axis of symmetry?

x = -3

x = 5

x = 1

x = 8

The average of -3 and 5 is 1

\frac{-3\ +\ 5}{2}\ =\frac{2}{2}\ =\ 1

x = 1 is the axis of symmetry

Poll

How do you feel about finding the axis of symmetry?

I got this!

With some practice I'll be good.

Whoa, I'm going to need a LOT of practice.

An axis of what??

Now that we can find the axis of symmetry

We can also find the vertex.

How?

Plug in the value of the axis of symmetry in for x and solve for y!

Multiple Choice

Find the zeros of the equation:
(x+10)(x-2) = 0

10 and 2

-2 and 10

-10 and 2

-2 and -10

Now you know that the

zeros, roots, or x-intercepts

are -10 and 2, find the axis of symmetry

$\frac{-10+2}{2}=\frac{-8}{2}=\ -4$

Plug in -4 for x and solve for y
y = (x + 10)(x - 2)
y = (-4 +10)(-4 - 2)
y = (6)(-6)
y = -36
The vertex is (-4, -36)

What are the x-intercepts? 2 and 6

The average of 2 and 6 is 4
plug 4 in to equation

$y\ =\ x^{2\ }-8x\ +12$

y\ =\ 4^2\ -8\left(4\right)\ +\ 12

y\ =\ 16\ -\ 32\ +\ 12

y\ =\ -4

Vertex is (4, -4) Whew!

Multiple Choice

What is the vertex?

(4,-4)

(2,0)

(0,2)

(6,0)

You Try!!

Multiple Choice

What are the zeros of the parabola?

1, 5

3, -5

3, 0

-6, 1

Multiple Choice

What is the axis of symmetry?

x = 2

x = 3

x = 5

x = 1

Multiple Choice

If the factored form of this graph is

$y\ =\ \left(x-1\right)\left(x-5\right)$
What would your vertex be?

(3, 32)

(3, -4)

(3, -2)

Finding the Vertex from the X-intercepts

Factor and solve to find the x-intercepts
Find the axis of symmetry by finding the average of the x-intercepts
Plug the value of the axis of symmetry in for x and solve for y.
Your (x, y) is your vertex
I DID IT!!!

Multiple Choice

Factor the following quadratic expression:

x² + 10x + 24

(x + 6)(x + 4)

(x + 10)(x + 2)

(x + 8)(x + 3)

(x + 2)(x + 12)

Multiple Select

If your factors were (x+6)(x+4), find the x-intercepts (choose 2):

x² + 10x + 24 = 0

x = -6

x = -8

x = -4

x = -3

Multiple Choice

If the x-intercepts for this equation are -6 and -4 what is the axis of symmetry?

x² + 10x + 24 = 0

x = -10

x = -5

x = 10

x = 8

Multiple Choice

If the axis of symmetry is x = -5, what is the vertex?

x² + 10x + 24 = 0

(-5, -51)

(-5, 84)

(-5, -1)

(-5, -36)

Did you get it right??

Practice makes perfect.

Follow the steps and you will get there.

Poll

I know how to find the axis of symmetry and the vertex for a quadratic using the x-intercepts.

100% True

75% True

50% True

Not yet BUT I WILL!!!

Finding the Vertex from Roots

You now know how to find the x-intercepts from factoring. Now we will use the x-intercepts to find the vertex.

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