AIM: What is the vertex form of a quadratic equation?
LAUNCH: For each quadratic function, determine the following pieces of information.
(a) What are the roots?
Do this by factoring and solving then double check your work with the graphing calculator
(b) What is the vertex for each equation?
1. x2 + 8x + 7
2. x2 + 8x – 20
3. x2 + 8x – 48
4. x2 – 14x + 40
5. x2 + 4x – 5
6. x2 + 10x + 16
(c) What is the parent function for each of the functions?
(d) What is the vertex for the parent function?
(e) Go back and describe how each vertex was transformed to become the new vertex from the
vertex of the parent function.
(f) Express each of these transformations using an equation.
PRACTICE:
1. For the following quadratics:
(a) Determine the vertex.
(b) Describe the transformations that occur from the parent function f(x) = x2.
(A) f(x) = 3(x – 4)2 + 6
(B) f(x) = -2(x + 9)2 – 5
2. Convert the following quadratic equations into vertex form.
(A) y = x2 − 6x + 5
(B) y = x2 − 2x − 5
(C) f(x) = (x + 7)2 – 4
3. Describe the transformations that occur from the parent function f(x) = x2.
(𝐴) 𝑓(𝑥) = (𝑥 + 2)2 − 1
(B) 𝑓(𝑥) = −2𝑥 2 + 3
1
(C) 𝑓(𝑥) = 3 (𝑥 − 5)2 + 1
(D) 𝑓(𝑥) = −(𝑥 + 3)2 − 2
(E) 𝑓(𝑥) = 2(𝑥 − 6)2 + 3
4. Factor and solve the following functions:
(A) 16x2 – 25 = 0
(B) 2x2 – 9x = -9
(C) 12 – 4x = x2