Algebra  1  –Day  10                                                                Name:  Vertex Form - Notes

Main Idea/Questions Notes/Examples

What is Vertex Form?

Vertex Form: 𝒚 = 𝒂 𝒙− 𝒉 𝟐 + 𝒌 where (h, k) is the vertex of the parabola

Standard Form of the

parabola

𝒚 = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄

Remember: The axis of symmetry divides the parabola in half AND goes through the

vertex.      𝑥 =  !!!!

Find the values of a, b, & c … … and the axis of symmetry

1. 𝑦 =  𝑥! − 4𝑥 + 4 a = _______ b = _______ c = _______        !!!!

= _________

2. 𝑦 =  𝑥! + 6𝑥 + 8 a = _______ b = _______ c = _______        !!!!

= _________

3. 𝑦 =  −3𝑥! − 12𝑥 − 8 a = _______ b = _______ c = _______        !!!!

= _________

4. 𝑦 =  2𝑥! + 12𝑥 + 19 a = _______ b = _______ c = _______        !!!!

= _________

Vertex Form 𝒚 = 𝒂 𝒙 − 𝒉 𝟐 + 𝒌

Find the h value…

1. 𝑦 = (𝑥 − 2)! h = _______ 2. 𝑦 = (𝑥 + 3)! − 1 h = _______ 3. 𝑦 = −3(𝑥 + 2)! + 4 h = _______ 4. 𝑦 = 2(𝑥 + 3)! + 1 h = _______

Making Connections: What do we know about the x-coordinate of the vertex? Compare the values for (-b/2a) and h in each example above. What do you notice? What does (-b/2a) represent in the parabola? So what does h represent in the parabola? What do you think k represents?

Practice: Find the vertex for the following quadratics functions.

5. y = (x - 3)2 + 4 Vertex: (_______, _______)

7. 𝑓(𝑥) =  𝑥! − 2 Vertex: (_______, _______)

6. y = 2(x + 1)2 – 12 Vertex: (_______, _______)

Algebra  1  –Day  10                                                                Name:  Vertex Form - Notes Main Idea/Questions Notes/Examples

Rewrite Equations

from Vertex to Standard

Form

What you know how to do: PEMDAS. How do we get from 𝑦 = (𝑥 − 2)! to 𝑦 =  𝑥! − 4𝑥 + 4? Start with : 𝑦 = (𝑥 − 2)! Rewrite the right side of the equation using TWO sets of parenthesis: Multiply using FOIL, Box, or Double Distribution: Collect like terms: Rewrite in Standard Form, if not in correct order already…. Now try these…. 𝑦 = (𝑥 + 3)! − 1 𝑦 = −3(𝑥 + 2)! + 4 𝑦 = 2(𝑥 + 3)! + 1 ** To check that you simplified correctly, you can enter both equations into your calculator and look at the table of values and/or graphs **

Algebra  1  –Day  10                                                                Name:  Vertex Form - Notes

Main Idea/Questions Notes/Examples

Write equations

given the vertex

and another point

on the graph

A quadratic function can be found if you know….

1. the vertex AND 2. one other point on the graph.

Write the equation of the parabola pictured to the right. Start with vertex form: 𝒚 = 𝒂 𝒙− 𝒉 𝟐 + 𝒌 Vertex from graph is ( _____ , ______) So… h = ________ and k = __________ What is the other point we are given? ( ________, ________) So… x = ________ and y = __________ Substitute these values into the Vertex Form of the equation….

____ = 𝒂 ___− ____ 𝟐 + ___ Solve for a …. The equation of the parabola is ______________________________ Now try this one…. Vertex: __________ h = ______ and k = _______ Other point: __________ x = ______ and y = _______

Algebra  1  –Day  10                                                                Name:  Vertex Form - Notes

The equation of the parabola is ______________________________