Algebra IUnit 8 mid-unit

Review

Unit 8 mid-unit Review

1. Given a quadratic function in vertex form: f(x) = -3(x + 5)2 – 4

Which of the following statements are true?

a) Adding 8 to the function shifts the graph up yes no

b) The graph of the function opens down yes no

c) The vertex is at the point (5, -4) yes no

d) Changing the 5 in the function makes the graph wider yes no

Unit 8 mid-unit ReviewAnswer

Pairs are: A & D, B & H, and F & G

1. Given a quadratic function in vertex form: f(x) = -3(x + 5)2 – 4

Which of the following statements are true?

a) Adding 8 to the function shifts the graph up yes no

b) The graph of the function opens down yes no

c) The vertex is at the point (5, -4) yes no

d) Changing the 5 in the function makes the graph wider yes no

Unit 8 mid-unit Review

2. A diver jumps from a diving board that is 10 feet above the water. She reaches the peak of her dive 0.875 seconds after leaving the diving board and she is 22.25 feet above the water. She is still 16 feet above the water 1.5 seconds after the jump.

 Write a function in vertex form to model the relationship between time from the beginning of the jump (x) and the height of the diver above the water (y).

Unit 8 mid-unit ReviewAnswer

Vertex at (0.875, 22.25)

y = a(x – 0.875)2 + 22.25

Use point on parabola (1.5, 16)

16 = a(1.5 – 0.875)2 + 22.25

.390625a = -6.25

a = -16

So, y = -16(x – 0.875)2 + 22.25

2. A diver jumps from a diving board that is 10 feet above the water. She reaches the peak of her dive 0.875 seconds after leaving the diving board and she is 22.25 feet above the water. She is still 16 feet above the water 1.5 seconds after the jump.

 Write a function in vertex form to model the relationship between time from the beginning of the jump (x) and the height of the diver above the water (y).

Unit 8 mid-unit Review

3. Write the equation in vertex form. 

y = -3x2 + 12x – 8

Unit 8 mid-unit ReviewAnswer

Axis of symmetry:

x = -b/(2a) = -12/((2)(-3) = 2

y-coordinate of vertex:

y = -3(2)2 + 12(2) – 8 = 4

So vertex is at (2, 4)

Equation: y = -3(x – 2)2 + 4

3. Write the equation in vertex form. 

y = -3x2 + 12x – 8

Unit 8 mid-unit Review

4. Find the x-intercepts. 

y = 4(x – 5) 2 – 36

Unit 8 mid-unit ReviewAnswer

x = 2 or 8

(2, 0) or (8, 0)

4. Find the x-intercepts. 

y = 4(x – 5) 2 – 36

Unit 8 mid-unit Review

5. Solve this equation. Give exact answer (simplest radical form). 

0 = -x2 + 10x + 2

Unit 8 mid-unit ReviewAnswer

5. Solve this equation. Give exact answer (simplest radical form). 

0 = -x2 + 10x + 2