Use finite differences to determine whether each relation is linear, quadratic, or neither.
Use finite differences to determine whether each relation is linear, quadratic, or neither.
Sketch the graph of the quadratic relation. Describe the transformation from the graph of y = x^2.
\displaystyle
y =x^2 + 2
Sketch the graph of the quadratic relation. Describe the transformation from the graph of y = x^2.
\displaystyle
y = (x + 3)^2
Sketch the graph of the quadratic relation. Describe the transformation from the graph of y = x^2.
\displaystyle
y =- \frac{1}{4}x^2
Dianne dove from the 10-m diving board. Her height h, in metres, above the water when she is x metres away from the end of the board is given by h = -(x - 1]^2 + 11.
a) Sketch a graph of her dive.
b) What was her maximum height above the water?
c) What horizontal distance had she travelled when she entered the water? Answer to the nearest tenth of a metre.
Determine an equation to represent the parabola in the form y = a[x - r)(x - s).
Evaluate.
2^{-4}
Evaluate.
(-3)^{-2}
Evaluate.
25^{0}
Evaluate.
8^{-1}
Evaluate.
(-1)^{12}
Evaluate.
(\frac{3}{4})^{-3}
Cobalt—60 is a radioactive element that is used to sterilize medical equipment.
Cobalt-60 decays to \frac{1}{2}, or 2^{-1}. of its original amount after every 5.2 years. Determine the remaining mass of 20 g of cobalt-60 after
a) 20.8 years
b) 36.4 years
Write an algebraic expression to represent the area of the figure. Expand and simplify.
Expand and simplify.
\displaystyle
(n+ 3)(n -3)
Expand and simplify.
\displaystyle
(h + 5)^2
Expand and simplify.
\displaystyle
(d-4)(d-2)
Expand and simplify.
\displaystyle
(m +3)(m + 7)
Expand and simplify.
\displaystyle
(3t -5)(3t + 5)
Expand and simplify.
\displaystyle
(x - 7)^2
Expand and simplify.
\displaystyle
x(3x + 1)(2x - 5)
Expand and simplify.
\displaystyle
(2k + 3)^2 -k(k+ 2)(k -2)
Expand and simplify.
\displaystyle
5(y-4)(3y + 1) + (3y -4)^2
Expand and simplify.
\displaystyle
3(2a + 3b)(3a -2b)
The area of a rectangle is given by the expression 8x^2 + 4x. Draw diagrams to show the possible rectangles, labelling the length and width of each.
Factor, if possible.
\displaystyle
y^2 + 12y + 27
Factor, if possible.
\displaystyle
x^2 + 2x -3
Factor, if possible.
\displaystyle
n^2 + 22n + 21
Factor, if possible.
\displaystyle
p^2 -8p + 15
Factor, if possible.
\displaystyle
x^2 + 2x - 15
Factor, if possible.
\displaystyle
k^2 -5k + 24
Factor.
\displaystyle
p^2 + 12p + 36
Factor.
\displaystyle
9d^2 -6d + 1
Factor.
\displaystyle
x^2 - 49
Factor.
\displaystyle
4a^2 -20a + 25
Factor.
\displaystyle
8t^2 -18
Factor.
\displaystyle
a^2 -4b^2
Find the value of k so that each trinomial can be factored over the integers.
\displaystyle
m^2 + km + 10
Find the value of k so that each trinomial can be factored over the integers.
\displaystyle
9a^2 -a + 4
The area of a circle is given by the expression \pi(4x^2 + 36x + 81). What expression represents the diameter of this circle?
A quadratic relation has roots 0 and -6 and a maximum at (-3, 4). Determine the equation of the relation.
The perimeter of a rectangle is 8 m and its area is 2 m^2. Find the length and width of the rectangle to the nearest tenth of a metre.
A ferry operator takes tourists to an island. The operator carries an average of 500 people per day for a round-trip fare of $20. The operator estimates that for each $1 increase in fare, 20 fewer people will take the trip. What fare will maximize the number of people taking the ferry?