Question

A.

5. y = -4(x - 2)² + 4 6. g(x) = 2(x + 1)² - 3
ses 1-12, graph the function. Label the vertex and axis of symmetry. (See Example 1.)
1.) f(x) = (x - 3)²
2. h(x) = (x + 4)²
9. y = -4(x + 2)² +1 10. y = ¹/(x-3)² + 2
MY
2
2.
STRUCTURE In Exercises 13-16, use the axis of symmetry to match the equation with its graph.
3. y = 2(x - 3)² + 1
14. y = (x +4)² - 2
15. y = (x + 1)² + 3
4
x = 2
6 x
B.
x = -1
-4-2
6
4
2
y
▶3. g(x) = (x + 3)² + 5 4. y = (x-7)² - 1
2 x
7. h(x) = 4(x + 4)² + 6
11. f(x) = 0.4(x - 1)² 12. g(x) = 0.75x² - 5
C.
4
АУ
Ay A
2
8. f(x) = -2(x - 1)² - 5
x = 3
2 4
X
16. y = (x - 2)² - 1
D.
-6
X = -4
2
B
АУ
-2
X

Answer 1

To graph the given functions and find the vertex and axis of symmetry, we can follow these steps:

1. Function: y = -4(x - 2)² + 4

- The vertex form of a quadratic function is given by y = a(x - h)² + k, where (h, k) represents the vertex.

- Comparing this with the given equation, we can identify the vertex as (2, 4).

- The axis of symmetry is a vertical line passing through the vertex, which is x = 2.

2. Function: g(x) = 2(x + 1)² - 3

- Again, comparing with the vertex form, we can identify the vertex as (-1, -3).

- The axis of symmetry is x = -1.

3. Function: f(x) = (x - 3)²

- The vertex form shows that the vertex is (3, 0).

- The axis of symmetry is x = 3.

4. Function: h(x) = (x + 4)²

- The vertex form reveals that the vertex is (-4, 0).

- The axis of symmetry is x = -4.

For the matching exercises:

3. Function: y = 2(x - 3)² + 1

- The vertex is (3, 1).

- The axis of symmetry is x = 3.

14. Function: y = (x + 4)² - 2

- The vertex is (-4, -2).

- The axis of symmetry is x = -4.

15. Function: y = (x + 1)² + 3

- The vertex is (-1, 3).

- The axis of symmetry is x = -1.