UI Algebra Equation for The Axis of Symmetry Question

Solve the equation: 722 + 4z – 2 = 0. Fully simplify all answers, including non-real solutions.
z =
Maytection
Consider the parabola given by the equation: f(x)
4×2 + 12x + 15
–
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.
61
5
3
2
1
-8
–
4
–
3
2
6
8
-2 -1
-1
-2
-3
-4
to
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
= 2
x2 – 12x + 27 into the form y
=
(x – h)? + k:
Answer: y =
Find the degree of the term – 3:
Find the degree of the term 6×5:
Find the degree of the term – 6×4:
Find the degree of the term 2×2:
Find the degree of the polynomial – 3 + 6×5 – 6×4 + 2×2:
Describe the end behavior (long run behavior) of f(x)
=
– x4
As x +
~, f(x) +
?
As x → 00, f(x) +v?
co
> Next Question
-00
0
Given the function f(x) = (x – 6)(x + 7)(x – 2)
its y-intercept is
its x-intercepts are
The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x = 2 and
0, and a root of multiplicity 1 at x = – 5.
=
Find a possible formula for P(x).
P(2)
=
The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 2 and a root of multiplicity 1 at
– 5. The y-intercept is y = – 12.
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
3
5
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5+
Q
y(x) =
You are working with a quadratic equation and constructing the following graph.
5
3
2
-2 -1
3
4
5
6
8
– 1
-2
-4
-5+
to
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 – 4)(x + 6)(x – 7)
its y-intercept is
its x-intercepts
are
Graph the function g(2)
– 0.5×2 + 4x – 10 on the axes below
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
1
2 3 4
5
6 7
8
9 10 11 12 13 14 15
15-14-13-12-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
-15+
Clear All Draw:
✓ AVO
Sketch the graph of y =
– (x – 3)2 + 1.
10
9
8
7
6
5
4
3
2
1
-10 -9 -8 -7 -6 -5 4 -3 -2 -1
– 1
1 2 3 4 5 6 7 8 9 10
-2
-3
-4
-5
-6
-7
-8
-9
-10
Clear All Draw:
FAVO
Given P(x) = x3 + 4×2 + 9x + 36. Write P in factored form (as a product of linear factors). Be
sure to write the full equation, including P(x) =
=
$5000 are invested in a bank account at an interest rate of 6 percent per year.
Find the amount in the bank after 6 years if interest is compounded annually.
Find the amount in the bank after 6 years if interest is compounded quaterly.
Find the amount in the bank after 6 years if interest is compounded monthly.
Finally, find the amount in the bank after 6 years if interest is compounded continuously.
Starting with the graph of f(x) = 64, write the equation of the graph that results when:
(a) f(a) is shifted 8 units upward. y =
(b) f(x) is shifted 9 units to the right. y
=
(c) f(x) is reflected about the y-axis. y =
=
Write the equation in exponential form.
Assume that all constants are positive and not equal to 1.
log, (c)
= m
Write the equation in exponential form.
Assume that all constants are positive and not equal to 1.
log(T) = m
Solve: log (y) = 3
Y =
Find the logarithm.
log2 ( 27
(2)-1
Find the logarithm.
log
1
10,000,000
II
Evaluate the following expressions. Your answers must be exact and in simplest form.
(a) Ine?
=
(b) eln5
=
10
(c) en v
=
(d) In
(*)
=
e5
Solve the system using substitution.
3x 5y =
– 14
7x + y = – 20
o One solution:
No solution
Infinite number of solutions
Solve the system by elimination.
3x
18
Зу
5y
— 4x +
— 29
One solution:
No solution
O Infinite number of solutions
Solve the system.
– 62 – 2g =
– 16
– 9x – 3y
–
– 25
The admission fee at an amusement park is $3.75 for children and $5.40 for adults. On a certain
day, 240 people entered the park, and the admission fees collected totaled $1131. How many
children and how many adults were admitted?
number of children equals
number of adults equals
Solve the System. Give answer as (x, y, z).
5x – 5y + z = – 22
10x + 5y + 32 – 16
– 20x + 5y + 4z
=
= 42
(x, y, z)
=
A movie theater has a seating capacity of 193. 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 $ 1400, How many children, students, and adults attended?
children attended.
students attended.
adults attended.
Write the system of equations as an augmented matrix.
4т +
2а
4и
10
2т +
За
Зи =
12
7т +
За
Би
=
42
1 4
Find the determinant of matrix A =
(-34
– 3 4
det(A) =
Solve the following system of equations using Cramer’s Rule:
=
6
2 + 3y
6x + 4y
=
– 20
Answer:(