University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

351

Pages:

3
Author:

Sonia Hayden

Graphing f(x) = a * x ^ 2 + c Core Concepts Graphing . When c > 0 the graph of f(x) = a * x ^ 2 + c is a vertical translation e units up of f(x) = a * x ^ 2 4 When c < 0 the graph of f(x) = a * x ^ 2 - c a vertical translation |c| units f(x) = a * x ^ 2 4y Vertex x Vertex. The vertex of the graph of f(x) = a * x ^ 2 + c (0, c), and the axis of symmetry is x = 0 Extra Practice has not Changed In Exercises 1-4, graph the function. Compare the graph to the graph of f(x) = x ^ 2 g(x) = x ^ 2 + 5 Xx² x integrate a(x) = x ^ 2 + 5 dx ups -24 -2 (- 2) ^ 2 + 5 = (4) + 5 = 9 Vertex (0,5) 11 00 -1 (- 1) ^ 2 + 5 =(1^ prime +5:6 AoS x = 0 2400 (0') ^ 2 + 5 = (0) + 5 = 5 Should be able to figure this out from the tion 1 (1) ^ 2 + 5 = (1) + 5 = 6 2 (2) ^ 2 + 5 = (4) + 5 = 4 24 3 (5) ^ 2 + 5 = 5 + 5 = |5| 2. m(x) = x ^ 2 - 3 down 3 -2 \ -2)^ 2 - 3z(1) + 3 = 1 Vertex (0,-3) -1 (- 1) ^ 2 - 3 = (1) - 3 = - 2 Aos x = 0 0 (2) ^ 2 - 3 = (0) - 2 = - 3 -2 2 4 1 (1) ^ 2 - 3 = (1) - 3 = - 2 2 (2) ^ (1/2) - z = (4) - 5 = 1 3 (3) ^ 2 - 3 = (9) * 3 = 6 8.2 3. n(x) = - 3x ^ 2 - 2 doun 2 vertical stretch b_{7} doun facing... so 3-2 0 reflect on x-axis Vertex (0-2) x = 0 n(x) = - 3x ^ 2 - 2 - 3 * (- 2) ^ 2 - 2 = - 3(4) - 2 = - 12 - 2 = - 14 - 3 * (- 1) ^ 2 - 2 = - 3(i) - 2 = - 3 - 2 = - 5 - 3 * (0) ^ 2 - 2 = - 3(0) - 2 = 0 - 2 = - 2 - 3 * (1) ^ 2 - 2 = - 3(1) * 2 = - 3 - 2 = - 5 ( - 3 * (2) ^ 7 - 2 = - 3(4) - 2 = - 12 - 2 = - 14 16 -201 2 -2 4. q(x) = 1/2 * x ^ 2 - 4 down 4 vertical shrink by 1/2 vertex (0,-4) AoS x = 0 x * 19(x) = 1 2 (x^ 2 -4 -2 1 1/2 * (- 2) ^ 2 - 4 = 1/2 * (4) - 4 = 2 - 4 = - 2 ( 1/2 * (- 1) ^ 2 - 4 = 1/2 * (1) - 4 = 0.5 - 4 = - 35 1/2 * (0) ^ 2 - 4 = 1 2 (0)-b|=0-h|=-h| 1/2 * (1) ^ 2 - 4 = 1/2 * (1) - 4 = 0.5 - 4 = - 35 2 1/2 * (2) ^ 4 - 4 = 1/2 * (4) - 4 = 2 - 4 = - 2 3 1/2 * (3) ^ 2 - 4 = 1/2 * (9) - 4 = 4 ,5-4=,5 In Exercises 5-8, find the zeros of the function. 4 5. y = - x ^ 2 + 1 0 = - x ^ 2 + 1 this means Factor and Solve 6. y = - 4x ^ 2 + 16 2 x ^ 2 = 1 See next Page 7. n(x) = - x ^ 2 + 64 8. p(x) = - 9x ^ 2 + 1