completeing the square cred
If the discriminant of a quadratic equation is equal to mc027-1.jpg, which statement describes the roots?
There are two complex roots.
How many solutions exist for the mixed-degree system graphed below?
1
Which phrase best describes the translation from the graph y = 6x2 to the graph of y = 6(x + 1)2?
1 unit left
How many solutions exist for the mixed-degree system graphed below?
2
Amira is solving the equation x2 - 6x = 1. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?
9
Consider the following system of equations.
The graphs of the equations intersect each other at two places.
The vertex of a parabola is in the first quadrant of a coordinate grid. A line with a negative slope passes through the origin. If the parabola and line intersect at the origin, which statement must be true?
The parabola opens downward.
Which equation is the inverse of y = 100 - x2?
a
If fx = x-3, which inequality can be used to find the domain of f(x)?
b
What is the domain of the function y=sqr x+6-7
b
Which equation is y = (x + 3)2 + (x + 4)2 rewritten in vertex form?
b
If mc016-1.jpg, which inequality can be used to find the domain of f(x)?
c
What is the domain of the square root function graphed below?
d
Which equation can be simplified to find the inverse of y = 2x2?
d
The graph of an equation with a negative discriminant always has which characteristic?
no x-intercept
Christian is rewriting an expression of the form y = ax2 + bx + c in the form y = a(x - h)2 + k. Which of the following must be true?
the value of a remains the same
Solve for mc019-1.jpg in the equation mc019-2.jpg.
x -7 +8i
Solve for mc016-1.jpg in the equation mc016-2.jpg.
x 5+ 35
Solve for mc011-1.jpg in the equation mc011-2.jpg.
x = -1 + 17
Solve for mc010-1.jpg in the equation mc010-2.jpg.
x = -16 or x -4
What are the solutions of the equation mc028-1.jpg?
x = 3 or -7
Which equation has the solutions mc012-1.jpg?
x2 + 3x + 3 = 0
Pablo graphs a system of equations. One equation is quadratic and the other equation is linear. What is the greatest number of possible solutions to this system?
2
Which equation can be solved using the expression mc003-1.jpg for x?
2 = 3x + 10x2
What is the discriminant of 9x2 + 2 = 10x?
28
What is the first step when rewriting y = 3x2 + 9x - 18 in the form y = a(x - h)2 + k?
3 must be factored from 3x2 + 9x
Which phrase best describes the translation from the graph y = 2(x - 15)2 + 3 to the graph of y = 2(x - 11)2 + 3?
4 units to the left
Which equation could be used to solve the following system?
4(11 - y)2 - 3y2 = 8
What is the first step when rewriting y = 6x2 + 18x + 14 in the form y = a(x - h)2 + k?
6 must be factored from 6x2 + 18x
What is the discriminant of 3x2 + 6x = 2?
60
Which value must be added to the expression x2 + 16x to make it a perfect-square trinomial?
64
Using the quadratic formula to solve x2 = 5 - x, what are the values of x?
a
Which equation can be simplified to find the inverse of y = 5x2 + 10?
a
Which graph shows the system mc021-1.jpg?
a
Solve for mc018-1.jpg in the equation mc018-2.jpg.
a x = 2 + 42
What are the solutions of the following system? -5
c
Which system is equivalent to mc005-1.jpg? y=x-2
c
Use completing the square to solve for mc024-1.jpg in the equation mc024-2.jpg.
c x = 1 + 89
Parabola A can be represented using the equation (x + 3)2 = y, while Line B can be represented using the equation y = mx + 9. Isabel determines one solution to the system of two equations must always pass through the vertex of Parabola A.
c. Isabel is incorrect because the point of intersection between Line B and Parabola A that can be determined is the y-intercept of the functions, not necessarily the vertex.
Which equation is the inverse of 5y+4=(x+362+1/2
d
Which equation is the inverse of y = 16x2 + 1?
d
Which equation shows the quadratic formula used correctly to solve 7x2 = 9 + x for x?
d
Solve for mc022-1.jpg in the equation mc022-2.jpg.
d x= 1 + 47
Which equation has a graph that is a parabola with a vertex at (-1, -1)?
y = (x + 1)2 - 1
Which equation has a graph that is a parabola with a vertex at (-2, 0)?
y = (x + 2)2
Which equation has a graph that is a parabola with a vertex at (5, 3)?
y = (x - 5)2 + 3
Which equation could generate the curve in the graph below?
y = -2x2 - 16x- 28
Which pair of equations generates graphs with the same vertex?
y = -4x2 and y = 4x2
Which equation could generate the curve in the graph below?
y = 3x2 - 2x + 1
