Answers Integrated Math 2A - Mr. Katykhin 26Solving Linear-Quadratic Systems

Solving Linear-Quadratic Systems — Unit test Answers

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Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?

{–7, 1}

(negative 3 minus StartRoot 10 EndRoot comma negative 3 + StartRoot 10 EndRoot)

(3 minus StartRoot 10 EndRoot comma negative 3 + StartRoot 10 EndRoot)

{1, 7}

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A quadratic equation of the form 0 = ax2 + bx + c has one real number solution. Which could be the equation?

0 = 2x2 – 4x + 1

0 = 2x2 – 5x + 3

0 = –2x2 – 4x – 2

0 = –2x2 – 3x – 1

Which is the graph of a quadratic equation that has a negative discriminant?

On a coordinate plane, a parabola opens down. It goes through (negative 4, negative 4), has a vertex at (negative 2, 0), and goes through (0, negative 4).

On a coordinate plane, a parabola opens down. It goes through (negative 4, negative 4), has a vertex at (negative 2, 0), and goes through (0, negative 4).

On a coordinate plane, a parabola opens up. It goes through (negative 4, 4), has a vertex at (negative 2, 0), and goes through (0, 4).

On a coordinate plane, a parabola opens up. It goes through (negative 4, 8), has a vertex at (negative 2, 4), and goes through (0, 8).

Fiona is completing the square to solve the polynomial equation.x2 – 4x + 1 = 0

isolating the constant 1

adding 4 to both sides of the equation

isolating the second term, –4x

adding 1 to both sides of the equation

Solve x2 − 24x = −80 by completing the square.What is the solution set of the equation?

{2, 40}

{4, 20}

{5, 16}

{8, 10}

Which function has real zeros at x = −10 and x = −6?

f(x) = x2 + 16x + 60

f(x) = x2 − 16x + 60

f(x) = x2 + 4x + 60

f(x) = x2 − 4x + 60

Mischa wrote the quadratic equation 0=-x2+4x-7 in standard form. If a = -1, what is the value of c in her equation?

c=-7

c=-1

c=4

c=7

The first few steps in solving the quadratic equation 5x2 + 27x = 14 − 13x by completing the square are shown.5x2 + 27x = 14 − 13x5x2 + 40x = 145(x2 + 8x) = 14

5(x2 + 8x + 16) = 30

5(x2 + 8x + 16) = 94

5(x2 + 8x + 4) = 18

5(x2 + 8x + 4) = 34

The function g(x) is defined as g(x) = 6x2 + 23x – 4. When does g(x) = 0?

x = –6 or x =

x = –4 or x =

x = or x = 6

x = or x = 4

The first two steps in determining the solution set of the system of equations, y = –x2 + 4x + 12 and y = –3x + 24, algebraically are shown in the table. Which represents the solution(s) of this system of equations?

(3, 15)

(–4, 36)

(3, 15) and (4, 12)

(–3, 33) and (–4, 36)

Solve x2 – 8x = 20 by completing the square. Which is the solution set of the equation?

{–22, 14}

{–14, 22}

{–10, 2}

{–2, 10}

A rectangle’s length is 5 inches more than twice its width. Its area is 50 square inches. Which equation can be used to find its width, w?

2w(2w + 5) = 50

2w(w + 5) = 50

w(2w + 5) = 50

w(w + 5) = 50

Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is –99.

(m – 5)(m + 5) = 99

(m – 10)(m + 10) = 99

m2 – 25 = –99

m2 – 100 = –99

What is the value of the discriminant of the quadratic equation −2x2 = −8x + 8, and what does its value mean about the number of real number solutions the equation has?

The discriminant is equal to 0, which means the equation has no real number solutions.

The discriminant is equal to 0, which means the equation has one real number solution.

The discriminant is equal to 128, which means the equation has no real number solutions.

The discriminant is equal to 128, which means the equation has two real number solutions.

What are the solutions to the quadratic equation 4(x + 2)2 = 36

x = −11 and x = 7

x = −7 and x = 11

x = −5 and x = 1

x = −1 and x = 5

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Solving Linear-Quadratic Systems — Unit test Answers

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