completeing the square cred

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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


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