study set for quadratics test
what is the solution set of x^2 + 5x + 1 = 0?
( -5 + sqrt 21 / 2, -5 - sqrt 21 / 2)
what is the solution set of (3x - 1)^2 = 5?
( 1 + sqrt 5 / 3, 1 - sqrt 5 / 3)
the endpoints of the diameter of a circle are (-7, 3) and (5, 1). What is the center of the circle?
(-1, 2)
what is the vertex of the parabola whose equation is y = (x + 1)^2 +3?
(-1, 3)
what is the midpoint of the line segment whose endpoints are (-8, 12) and (-13, -2)?
(-10.5, 5)
which of the following points lies on the graph of y = x^2 - 2x + 6?
(-3, 21)
what is the solution set of 7x^2 + 3x = 0?
(0, -3/7)
what is the solution set of 2x(x - 1) = 3?
(1 + sqrt 7 / 2, 1 - sqrt 7 / 2)
what is the solution set of (x - 2)(x - 3) = 2?
(1, 4)
which of the following sets could be the sides of a right triangle?
(2, 3, sqrt 13)
which of the following points lies on the circle whose center is at the origin and whose radius is 10?
(5 sqrt 2, 5 sqrt 2)
find the midpoint of the line segment whose endpoints are (3, 10) and (7, 8).
(5, 9)
which of the following equations is the result of completing the square on x^2 - 6x - 9 = 0?
(x - 3)^2 = 18
which of the following equations is quadratic?
(x+3)(x+4) = 5
what is the x-coordinate of the vertex of the parabola whose equation is y = 3x^2 + 9x?
-1 1/2
the square of a certain negative number is equal to five more than one-half of that number. what is the number?
-2
if the quadratic formula is used to find the solution set of 3x^2 + 4x -2 = 0, what are the solutions?
-2 + sqrt 10 / 3
what is the value of b^2 - 4ac for the following: 2x^2 + 3x = -1
1
the center of a circle is at the origin. An endpoint of a diameter of the circle is at (-3, -4). How long is the diameter of the circle?
10
there is a direct path from Gayle's house to the store. Due to construction, the direct route is closed and Gayle must travel 6 miles east and then 8 miles north in order to get to the store. How long is the direct path from Gayle's house to the store?
10 miles
a circle has its center at the origin, and (5, -12) is a point on the circle. How long is the radius of the circle?
13
what is the length of the hypotenuse of a right triangle whose legs have lengths of 5 and 12?
13
a carpenter is framing a wall that is 8 feet high and 15 feet long. If the carpenter wants to be sure that the sides of the wall meet at right angles, then what should the diagonal measurement of the wall be?
17 feet
which of the following constants can be added to x^2 -10x to form a perfect square trinomial?
25
if the hypotenuse of a right triangle is 2 square root of 3 units long and one of the legs is units long, then how long is the other leg?
3
an object is dropped off a building that is 144 feet tall. after how many seconds does the object hit the ground? (s = 16t^2)
3 seconds
the width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches, then the area of the resulting rectangle is 24 square inches. what is the area of the original rectangle?
48 square inches
what number is midway between 2/5 and 1?
7/10
the graph of a quadratic equation opens down when the value of ___ is negative
a
give the values of a, b, and c from the general form of the equation (2x + 1)(x - 2) = 0
a = 2, b = -3, c = -2
describe the translation of the graph of y=x^2 that results in the graph of y = (x - 3)^2
right 3 units
what is the distance between the points (2, 5) and (5, 7)?
square root of 13
solve this quadratic equation; x^2 + 2x - 22 = 0
x = -1 + sqrt 23
solve this quadratic equation; x^2 + 5x + 3 = 0
x = -5 + sqrt 13 / 2
what is the line of symmetry for the graph of y = -3x^2 +12x - 11?
x = 2
find the line of symmetry for the parabola whose equation is y = 2x^2 - 4x + 1
x=1
what is the equation of a circle whose center is at the origin and whose radius is 16?
x^2 + y^2 =256
which of the following is the general form of the equation 5x^2 - 20x =15?
x^2 - 4x - 3 = 0