1. Lesson 5.4 Vertex Form

2. Vertex Form 𝒚=𝒂 𝒙−𝒉 𝟐 +𝒌  vertex form (h,k)  vertex point
Line of symmetry comes from
h x = h

3. Identify the vertex and the line of symmetry
𝒚=𝒂 𝒙−𝒉 𝟐 +𝒌
𝒚=−𝟒(𝒙−𝟑) 𝟐
𝒚=𝒙 𝟐 +𝟓
𝒚=−𝟒(𝒙+𝟑) 𝟐 +𝟔

4. Identify the vertex and the line of symmetry
𝒚=𝒂 𝒙−𝒉 𝟐 +𝒌
𝒚=𝟑(𝒙+𝟔) 𝟐
𝒚=−(𝒙) 𝟐
𝒚=−(𝒙−𝟑) 𝟐 −𝟓

5. Identify the vertex, the line of symmetry, and sketch
𝒚=𝒂 𝒙−𝒉 𝟐 +𝒌
𝒚=−𝟒(𝒙+𝟑) 𝟐

6. Identify the vertex, the line of symmetry, and sketch
𝒚=𝒂 𝒙−𝒉 𝟐 +𝒌
2. 𝒚=(𝒙−𝟐) 𝟐 +𝟒

7. Find the vertex form, the vertex point, and the line of symmetry 1) g(x) = 𝑥 2 −6𝑥 −2

8. Find the vertex form, the vertex point, and the line of symmetry 2) g(x)= 𝑥 2 −5𝑥

9. Find the vertex form, the vertex point, the line of symmetry, and sketch 3) g(x) = −𝑥 2 +6𝑥+13

10. Homework: #38-46 even 38. g(x) = 3𝑥 2 40. g(x)= 𝑥 2 −5𝑥
Write each quadratic function in vertex form, give the coordinates of the vertex, and the equation of the axis of symmetry.
38. g(x) = 3𝑥 2
40. g(x)= 𝑥 2 −5𝑥
42. g(x) = 𝑥 2 −6𝑥 −2
44. g(x) = 𝑥 2 +7𝑥+3
46. g(x) = −2𝑥 2 +12𝑥+13

11. Answer Key for the homework
38) y=3( 𝑥−0) 2 +0; 0,0 ;𝑥=0 40) y=( 𝑥− 5 2 ) 2 − 25 4 ; 5 2 , −25 4 ;𝑥= ) y=( 𝑥−3) 2 −11; 3,−11 ;𝑥=3 44) y=( 𝑥−( −7 2 )) 2 − 37 4 ; −7 2 , −37 4 ;𝑥= −7 2 46) y=−2( 𝑥−3) 2 +31; 3,31 ;𝑥=3