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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 ______________________________