Quadratic Functions
Name
Pre Calculus
Date
Find all related information and graph each function:
1. f(x) = x2 – 6x – 8
Vertex
Axis of symmetry
Y-intercept
X-intercepts
2. Y = (x – 2)2
Vertex
Axis of symmetry
Y-intercept
X-intercepts
6th Block
Quadratic Functions
Pre Calculus
Find the x intercepts of the following:
3. F(x) = x2 + 8x + 9
4. G(a) = a2 – 15a + 36
5. 0 = -2(c + 18)(c – 10)
Part I: Identify the vertex, the axis of symmetry, the maximum or minimum value, and the y
intercept of each parabola given standard form.
1. y = x2  4x + 1
2. y = x2 + 2x + 3
Vertex
Vertex
Axis
Axis
Max or Min
Max or Min
Y intercept
(0,
3. y = x2  6x  10
)
Y intercept
4. y = 3x2 + 4x
Vertex
Vertex
Axis
Axis
Max or Min
Max or Min
Y intercept
Y intercept
Quadratic Functions
Pre Calculus
Part II: Identify the vertex, the axis of symmetry, the maximum or minimum value, and the y
intercept of each parabola given vertex form.
For each function, find the y-intercept.
5. y = (x + 3)2  5
6. y = 2(x  2)2 + 6
Vertex
Vertex
Axis
Axis
Max or Min
Max or Min
Y intercept
Y intercept
7. y = (x + 1)2 + 9
8. y 
Vertex
Vertex
Axis
Axis
Max or Min
Max or Min
Y intercept
Y intercept
1
2
 x  4  15
2
Part II: Sketch each parabola using the given information.
9. Vertex (4, 2), y–intercept 6
10. vertex (3, 12), point (1, 0)
Quadratic Functions
Pre Calculus
Graph each function.
12. y = (x + 3)2 + 10
11. y = x2 + 8x +8
Part V:
Simplify each number in terms of i.
1.
49
2.
144
3.
48
Simplify each expression:
6. (6 - 7i) - (6  7i)
7. i4
8. i2(-3 + 4i)
9. (4  3i)(5 + 4i)
Quadratic Functions
13. 3i(2 + 2i)
Pre Calculus
14. (5 + 3i)  3(8 + 2i)
15. (2  i2)(3 + 6i)
Write the conjugate of each complex number in the space provided.
16. 2 – i
17. -18 – 2i
18. -6i + 8
Rationalize each denominator.
16.
5  2i
4i
18. 3i/2+i
20. (6i – 5)/(-2-3i)
17.
19.
3  2i
4  3i
7
5  2i
21. (-2i + 3)/(2+i)
Quadratic Functions
Pre Calculus
Short answer:
1. What is the vertex form of a quadratic function?
2. What is the standard from of a quadratic function?
3.
Synthesis: Write a quadratic equation for a parabola whose vertex is in the 3rd quadrant.
What are the vertex, the axis of symmetry, the maximum or minimum value, the domain, and the
range of each function? Label your answers neatly and carefully!
5. f(x) = 2(x  4)2 + 3
6. f(x) = (x + 3)2  2.5
Vertex
Vertex
Axis of Symmetry
Axis of Symmetry
Max or Min
Max or Min
Domain
Domain
Range
Range
Quadratic Functions
Pre Calculus
7. f(x) = 2(x  6)2
8. y = x2 + 5x  14
Vertex
Vertex
Axis of Symmetry
Axis of Symmetry
Max or Min
Max or Min
Domain
Domain
Range
Range