Use the function f(x)=x 2 −6x+8 to answer the following questions: a. What is the y-intercept? b. What are the x-intercepts? c. What is the vertex? d. What is the axis of symmetry?
Answers
Answer:
see explanation
Step-by-step explanation:
given the function
f(x) = x² - 6x + 8
(a)
to find the y- intercept , let x = 0 in f(x)
f(0) = 0² - 6(0) + 8 = 0 - 0 + 8 = 8 ← y- intercept
(b)
to find the x- intercepts , let f(x) = 0 , that is
x² - 6x + 8 = 0 ← in standard form
(x - 2)(x - 4) = 0 ← in factored form
equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x - 4 = 0 ⇒ x = 4
the x- intercepts are x = 2 and x = 4 or (0, 2 ), (0, 4 ) in coordinate form
(c)
given a quadratic in standard form
f(x) = ax² + bx + c ( a ≠ 0 )
then the x- coordinate of the vertex is
= -
f(x) = x² - 6x + 8 ← is in standard form
with a = 1 and b = - 6 , then
= -
= - (- 3) = 3
evaluate f(3) for corresponding y- coordinate
f(3) = 3² - 6(3) + 8 = 9 - 18 + 8 = - 9 + 8 = - 1
vertex = (3, - 1 )
(d)
the axis of symmetry is a vertical line , passing through the vertex with equation
x = c ( c is the value of the x- coordinate of the vertex )
equation of axis of symmetry is then x = 3
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Change 0.625 to a percent.
How many square tiles are needed to make a pattern of 6?
-4
-2
0
4
Answers
Answer:
-4
Step-by-step explanation:
The number inside of the ( ) for a log must be greater than 0.
Answers
DEFINITION
rhombus is a parallelogram with four sided equal a parallelogram whose all sides are equal is called a rhombus
PROPERTIES
- all side are equal length
- each pair of opposite sides are equal
- opposite angles are equal
- diagonals of a rhombus are perpendicular bisector each other
B. x2 + 14x + 49
C. x2 – 5x + 25
D. x2 – 24x + 144
E. x2 + 9x – 81
Answers
ax^2+bx+c such that
a=1
(b/2)^2=c
check each
all of them have 1 in front so skipt that step
A. (16/2)^2=8? false so no
B. (14/2)^2=49? true, this is
C. (-5/2)^2=25? false, this is not
D. (-24/2)^2=144? true, this is
E. (-9/2)^2=-81? false (easy way is that x^2 is never equal to a negative unless it is complex
B and D are answers
B. (x + 7)(x + 7) = Works
C. Doesn't work
D. (x - 12)(x - 12) = Works
E. Doesn't work
Therefore the answers are B and D
The other don't work because they do not become perfect squares.
Volume=4/81π ft^3
Answers
Answer:
(∛3)/2 ft = r
Step-by-step explanation:
Start with the formula for the volume of a sphere: V = (4/3)πr³. Solve this for r³ and then take the cube root of the result:
3V
V = (4/3)πr³ => (3/4)V = πr³ => (------- = r³
4π
3 · 4/81π ft^3 3 · 4π ft³ 3 ft³
Here we have r³ = -------------------- = ---------------- = -------------
4π 8(4π) 8
and so the radius is r = ∛[ (3/8) ft³] = (∛3)/2 ft = r
Answers
Answers
because there is a bracket in between the two expressions it means we have to multiply them together: (x-4) x (x-2)
you can break down the question into smaller parts:
x multiply x
x multiply -2
-4 multiply x
-4 multiply -2
here are the answers:
x^2 (means x squared)
-2x
-4x
8 (because when you multiply two negative numbers it makes a positive)
now you put it into an expression (this is expanding):
x^2 - 2x - 4x + 8
to simplify it you collect like terms:
x^2 - 6x + 8
The above is the answer :)