Properties of Graphs
Let g(x) = -x2 + 6x - 6. Find and simplify g(1/2).
- 13/4
Write the standard form of the equation of the circle of radius r = 10 and center (h, k) = (0, 0)
x2 + y2 = 100
Identify the slope and y-intercept of the line. Then, graph the line.
x + 6y = 6
Slope: -1/6, y-intercept: 1, Sketch y = -1/6x+1
Write P(x) = x2 + 12x in vertex form.
P(x) = (x+6)2 - 36
A rectangular parking lot has a length that is 8 yards greater than the width. The area of the parking long is 560 square yards. Find the length and the width.
Width: 20 yards
Length: 28 yards
Determine whether the equation defines y as a function of x.
y = 2/(x+6)
yes
Write the standard form of the equation of the circle with a radius of 3, centered at (0, -3).
x2 + (y + 3)2 = 9
Find the equation of the line that passes through the origin and (7, 8).
y = 8/7 x
Solve the quadratic equation using any method you wish.
9x2 - 6x + 1 = 0
{1/3}
If g(x) = -(x - 3)2 + 1, identify the vertex, axis of symmtery, and whether the graph is concave up or concave down?
Vertex: (3, 1)
Axis of symmetry: x = 3
Concavity: up
Find the domain of the given function in interval notation.
F(x)= (x-1)/(x3+x)
(-inf, 0)U(0, inf)
Find the center and radius then graph the circle.
2x2 + 2y2 = 128
Center: (0, 0)
Radius: 8
Graph
Solve the equation. The letters a, b, and c are constants.
ax - b = c
x = (b + c)/a
For the quadratic function f(x)= -x2 + 4x, identify each of the following:
a) Does the graph of f open up or down?
b) Vertex
c) Axis of Symmetry
d) Intercepts
e) Domain:
Range:
f) Increasing:
Decreasing:
a) down
b) (2, 4)
c) x=2
d) (0, 0), (4, 0)
e) D: (-inf, inf) / R: (-inf, 4]
f) inc: (-inf, 2) / dec: (2, inf)
Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value, and then find that value.
f(x)=-2x2+4x-11
maximum: -9
Algebraically determine if the following function is even, odd, or neither.
f(x)= -x3 + 2x2 +6x - 5
neither
Find the equation of the circle centered at the origin that passes through (-4, 7).
x2 + y2 = 65
Find an equation for the line with the given properties. Express your answer using either the general form or the slope intercept form of the equation of a line.
x-intercept = -2 ; y-intercept = 2
y = x + 2
Write 21(p2 - 1) = 40p in completely factored form. Then, identify the solutions.
(7p + 3)(3p - 7) = 0
{-3/7 , 7/3}
Solve the following equation by the square root method.
(x + 7)2 = 81
{-16, 2}
Find the domain of the function in interval notation:
f(x)= 6x/sqrt(x+8)
(-8, inf)
Find the center and radius of the circle whose endpoints of a diameter are at (2, 5) and (5, 5). Then, write the standard form of the equation.
Center: (3.5, 5)
Radius: 1.5
Equation: (x-3.5)2 + (y-5)2 = 2.25
Solve: (x+4)/5 + (x+2)/2 = 3
12/7
Determine the quadratic function f whose vertex is at (4, -1) and another point is (3, 2).
f(x) = 3x2 - 24x+47
A shoe store offers a 15% discount on a pair of shoes. If the sale price is $65, what was the original price of the shoes?
$76.47