Unit 4 Review

Unit 4 Review Put the following quadratics into vertex form then identify the vertex and axis of symmetry. Identify the transformations to the graph. 1.

f ( x)  2 x 2  4 x  3

2. j( x)  x 2  6 x  7

axis of symmetry:

axis of symmetry:

vertex:

vertex:

transformations:

transformations:

Graph the following questions in the provided axes. 3. y  2( x  5)2  2

4. y   x 2  6 x

axis of sym:____=_______; vertex (_____,_____)

axis of sym:____=_______; vertex (_____,_____)

x-intercepts:_______________;

x-intercepts:_______________;

y-int:_______

y-int:_______

For #5-6: Graph the following equations. Identify: the vertex, axis of symmetry, the x-intercepts, the y-intercept, domain, range and whether your vertex is a maximum or minimum. 5.

y  2 x2  8x  3

Axis of Sym: Vertex: x-ints (exact answer):

y-int: Domain in interval notation:________

Range in interval notation:_________ Vertex is a ________

6. j( x)  3( x  2)2  3 Axis of Sym:

Vertex:

x-ints:

y-int:

Domain in interval notation:________

Range in interval notation:_________ Vertex is a ________

7. The graph of g(x) is a transformation of the graph of f(x)= x2. If the vertex of the graph of g(x) is (5, -6) with a vertical stretch of 2 what is the equation of g(x) in vertex form?

8. Identify the x and y – intercepts of each function. (a) f ( x)  x 2  11x  30

9. Change to STANDARD FORM: y = ax2 + bx + c

(b)

f ( x)  4 x 2  14 x  8

Show steps.

. (a) y = -4(x – 3)2 – 2

(b)

y = 3(x + 8)2 + 7

10. An object fired upwards from the top of a 640 foot building has an initial velocity of 96 feet per second. The height of the object t seconds after firing is given by: h(t) = -16t2 + 96t + 640.

(a) Find the maximum height of the object and the time it takes to reach the maximum height.

(b) How long does it take for the projectile to hit the ground?

(c) Find the height of the projectile at 3 seconds.

11. Johnny wants to enclose a rectangular garden using 42 feet of fencing. He wants to maximize the area. What is the length and width he needs to accomplish this and what is the maximum area?