UI Intercept of The Parabola and Decimal Place Algebra Question

Solve the equation: 3m2 + 4m + 9 = 0. Fully simplify all answers, including non-real solutions.
m =
Consider the parabola given by the equation: f(x) = 4×2 – 10x – 7
Find the following for this parabola:
A) The vertex:
B) The vertical intercept is the point
C) Find the coordinates of the two x -intercepts of the parabola and write them as a list, separated
by commas:
It is OK to round your value(s) to to two decimal places.
You are working with a quadratic equation and constructing the following graph.
6+
5
4
-8-7-6
-4-3-2
3
4 5
6
7 8
– 1
-2
-3
-4
-5+
Identify the vertex of the parabola:
Remember that the vertex is a point!
Identify the y-intercept of the parabola:
Remember that the y-intercept is a point!
Identify the x-intercepts: and
Remember that the x-intercepts represent points on the graph!
Given the x-intercepts above, write an equation for the parabola in factored form:
y =
Hint: Think about the zero-product property.
Write an equation for the axis of symmetry:
Put the equation y
=
x2 + 10x + 24 into the form y = (ac – h)? + k:
Answer: y =
Find the degree of the term – 2.6:
Find the degree of the term – 1x”:
Find the degree of the term 3×3:
Find the degree of the term – 5:
Find the degree of the polynomial – 2×6 – 1×5 + 3×3 – 5:
Describe the end behavior (long run behavior) of f(x) =
=
208
As x +
00, f(x) +
?
As x +00, f(x) +
?
Given the function f(x) = (x – 3)(+ 2)(x – 6)
its y-intercept is
its x-intercepts are
–
– 3 and
The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x
0, and a root of multiplicity 1 at x = – 3.
=
Find a possible formula for P(x).
P(x) =
=
The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 1 and a root of multiplicity 1 at
3. The y-intercept is y – 1.8.
X =
=
Find a formula for P(x).
P(x) =
=
Write an expression in factored form for the polynomial of least possible degree graphed below.
5+
4
3
2
1
-5 -4
2
1
-1
-1
2
3
4
5
-2
-3
-4
-5+
Q
y(x) =
You are working with a quadratic equation and constructing the following graph.
61
5
4
3
2
1
4 5 6
7
8
-8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5+
Identify the vertex of the parabola:
Remember that the vertex is a point!
Identify the y-intercept of the parabola:
Remember that the y-intercept is a point!
Identify the x-intercepts: and
Remember that the x-intercepts represent points on the graph!
Given the x-intercepts above, write an equation for the parabola in factored form:
y =
Hint: Think about the zero-product property.
Write an equation for the axis of symmetry:
Given the function f(x) = (x − 2)(x + 1)(x – 7)
its y-intercept is
its x-intercepts are
Graph the function g(x) =
=
0.5×2 + 2x on the axes below
15+
114
13
12
11
110
9
8
7
6
5
4
3
2
1
15-14-13 -12 -11 -10 -5 -6 -7 -6 -5 -4 -3 -2 -1
2
3 4 5
6
7 8
9 10 11 12 13 14 15
– 1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
-15+
Clear All Draw:
JAVO
Sketch the graph of y = (x – 2)² – 4.
10+
9
8
74
6
5
4
اندا
2
1
-10 -9 -8 -7 -6 -5 -4 -3 -2
1 2 3 4 5 6 7 8 9 10
-2
-3
-4
-5
-6
-7
-8
-9
-10+
Clear All Draw:
Invo
The admission fee at an amusement park is $3.75 for children and $5.20 for adults. On a certain
day, 286 people entered the park, and the admission fees collected totaled $1232. How many
children and how many adults were admitted?
number of children equals
number of adults equals
A movie theater has a seating capacity of 181. The theater charges $5.00 for children, $7.00 for
students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket
sales was $ 1296, How many children, students, and adults attended?
children attended.
students attended.
adults attended.
Write the system of equations as an augmented matrix.
– 66 +
2d +
5c
34
– 76
2d +
4c
-51
– 2b +
6d
2c
40
ㄱ J
J
Find the determinant of matrix A
=
–4 – 5
– 3 0
det(A) =
Select all of the following tables which represent y as a function of x.
9
9 |
y
X
0
-5
بن ابM
1
1
8 | بن ابي | | | o
4
1
5
| | د ادم | سا
y
-3
2
6
8
16
ل بادام ایM
| بن ابي | مه | o
ل | | | | س
5
9
8
7
7
2
| O
The plot below represents the function f(2)
8
7
6
5
4
3
2
1
-5 -4 -3 -2 -1
-1
2 3 4 5
-2 +
Evaluate f(2)
f(2)
=
Solve f(x) = 2
2=
Match each graph with its equation.
=
y
22
7
1
6
–
y
= X
x2
5
4
=
–
(0) ข
vã
3
a.
–
Oy =
2
1
–
O y = |2|
-2 -1
1
-2.1
2
3
1
4 5 6 7
–
y
=
1-2
7+
6
5
4
3
b.
2
1
1
2
3
4 5 6
-2 -1
– 1
-2
7
6
5
4
3
C.
2
1
-2 -1
1
2
3
4 5
6 7
7
6
5
4
دیا
d.
2
1
1 2
3
4
-2 -1
– 1
5 6
-2
q 9
7
6
5
4
3
e.
2
1
-2 –
– 1
2
3
4
5 6
-2
d
7
6
5
4
3
f.
2
1
2
3
4
5 6
-2 -1
– 1
-2
q 9
What is the domain of the following function: f(x)
X + 1
X – 7
x + 7
(7,00)
[-1,0)
[ – 1,7) U (7,0)
All real numbers
=
Given f(x) x?, after performing the following transformations: shift upward 92 units and shift 5
units to the right, the new function g(x) =
=
Let
f(a) = 13x + 6
f-1(x) =
Describe the long run behavior of f(x) = x? – 5×5
3×3 + 3
As x +
oo, f(a) +
?
As x → 00, f(x) +
?
Write an equation (any form) for the quadratic graphed below
5+
4
3
2
1
-5 -4 -3 -2 -1
1
2
3
4
– 1
-2
-3
-4
-5+
q
y=
Consider the parabola given by the equation: f(x) = 4×2 – 8x – 12
Find the following for this parabola:
A) The vertex:
B) The vertical intercept is the point
C) Find the coordinates of the two x intercepts of the parabola and write them as a list, separated
by commas:
It is OK to round your value(s) to to two decimal places.
–
3 and
X =
The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at 3
0, and a root of multiplicity 1 at x = – 4
Find a possible formula for P(2).
P(x) =
Find the domain and range of the function graphed below.
5
4
3
2
1
3
4 5
-5 -4 -3 2-1
– 1
-2
-3
-4
-5+
Domain:
Range:
For each function, determine the long run behavior
x2 + 1
ha ✓ Select an answer
23 + 2
No horizontal asymptote
a Horizontal asymptote at y=0
ha
a Horizontal asymptote at y=1
x2 + 2
2
x” + 1
X3 + 1
X2 + 2
has Select an answer
< >
Consider the function in the graph to the right.
The function has a relative maximum of
at x =
10+
9
8
The function has a relative minimum of
7
6
at x =
5
4
The function is increasing on the interval(s):
2
1
-10 -9 -8 -7 -6 -5 -4 -3
-2
5
6
8
–
-1
9 / 10
-2
The function is decreasing on the interval(s):
-3
-4
-5
-6
The domain of the function is:
-7
-8
-9
-10
The range of the function is:
If log2 (4x + 3) = 3, then x
=
Find the logarithm.
log10(10, 000, 000)=
Evaluate the following expressions. Your answers must be exact and in simplest form.
(a) Ine’ =
(b) en 6
(c) en v2
=
(d) In
Solve for x: 4° = 17
X =
Solve for x:
log x + log(x + 3) = 8
X =
Solve the system using substitution.
38
– 4x — бу
– 2x + y = – 9
One solution:
O No solution
Infinite number of solutions
The admission fee at an amusement park is $4.25 for children and $5.40 for adults. On a certain
day, 335 people entered the park, and the admission fees collected totaled $1625. How many
children and how many adults were admitted?
number of children equals
number of adults equals
x3 + 7×2 + 13x + 9
Find the quotient and remainder using synthetic division for:
X + 2
The quotient is
The remainder is
Solve the System. Give answer as (x, y, z).
9
– 1x – 6y + 12
– 2x + 6y + 62
4x + 6y – 4z
-4
=
– 18
One or more solutions:
No solution
o Infinite number of solutions