Identifying Functions
A Relation can be defined using what?
1. A set of ordered points
2. A table of values
3. An equation
4. A Graph
5. Mapping diagram
Does f(x) mean f times x?
No
What is vertex form when solving quadratics?
y = a (x - h)2 + k
Does this Prabola have a Max or Min value?
https://www.varsitytutors.com/hotmath/hotmath_help/topics/parabolas
It has a minimum value because the Parabola faces up
What is the radical sign and what does it represent?
This is the radical sing : √ , and it goes above a positive square root of a number
How do you know if a relation is a function?
- The x values don't repeat in a table
- The graph passes the "vertical line test"
f(x) = x+16
Find f(1)
f(1) = 1+16
= 17
When completing the square, what do you do to find the magic number?
To find the magic number you take value b, multiply it by half, then square it:
Magic number: 0.5()2=
Will this Prabola have a Max or Min value?
y = 3(x-7)2 + 8
Min value because the a value is greater than 1
Express the following as a mixed radical in simplest form
√200
= √ 3 . 100
= √ 3 . √ 100
= 10 √3
If f(x) = x2-6x, find x if f(x) = 16
x = 8, x = -2
Solution:
f(x) = 16
32 = x2 - 6x
0 = x2 - 6x + 16
0 = (x-8) (x+2)
x-8 = 0 x+2 = 0
x=8 x=-2
Write the following equation in the form a(x-h)2+ k by completing the square. State the vertex, the min/max values and when it occurs:
f(x) = y = 4x2 + 16x - 5
f(x) = 4 (x2 + 4x) - 5
= 4 (x2 + 4x + 4 - 4) - 5
= 4 (x2 + 4x + 4) - 16 - 5
= 4(x + 2) - 21
V: (-2,-21)
Min: -21 when x is 2
Will the Parabola open up or down? State the max or min and when it occurs.
f(x) = -2(x+3)2 + 1
The Parabola will open downwards, and the max is 1 when x is 3
When adding and subtracting radicals you must have like radicals. Solve the following:
2√ 6 + 5√6 + 4√3
7√6 + 4√3
Solution:
2√ 6 + 5√6 + 4√3
= 7√ 6 + 4√3
State the Domain:
(3,4),(6,9),(4,2),(1,7)
3,6,4,1
If f(x) = x2 -11x, find the values of x if the value of f (x) is 12
f(x) = 12
12 = x2 - 11x
0 = x2 - 11x - 12
0= (x+12) (x-1)
x + 12 = 0 x - 1 = 0
x = -12 x = 1
We use Partial Factoring to find the...
Vertex of a Quadratic Function
Turn the following equation into vertex form, and state the max or min value:
f(x) = 16x2 + 32x + 12
V: 16 (x + 1 )2 - 4
Min = -4 when x is 1
Solve the following:
(2 + 6√3)(2 - 8√3) + 2√3
-140 - 2√3
State the Range:
g(x) = x2
(YER l y <or= 0)
If f(x) = 6x2 - 14, evaluate f (-6)
f(-6) = 6(-6)2-14
f = 6(32)-14
f =216 - 14
f = 202
Please do the following question on paper because only the answer will be shown.
Determine the vertex of the following function:
y = x2 + 2x - 3
V: (-1,-4)
State the following:
The direction of opening:
Coordinates of Vertex:
Axis of Symmetry:
Max/Min value:
Domain:
Range:
Up
(-3,-2)
x = -3
y = -2 (min)
{XER}
{YER l y > or = -2}
Solve the following:
√560 / √80
= 7