factor: |
(verb) to break up a polynomial into a product of polynomials that can be multiplied to get the original polynomial |

root: |
(noun) an x-value where the polynomial function intersects the x-axis; the x-values where f(x) = 0 |

zero of a function: |
(noun) a value of the independent variable in a function that results in a value of zero for the dependent variable |

zero product property : |
(noun) the property stating that if a product is equal to zero, then at least one of the factors must be zero |

Which statement describes the graph of f(x) = 4×2 + 20x + 25? |
XX The graph intersects the x-axis at (2, 0) and (5, 0). |

A function g(x) has x-intercepts at (1/2, 0) and (6, 0). Which could be g(x)? |
XX g(x) = 2(x + 1)(x + 6) |

The only solution of the equation x2 + bx + 16 = 0 is x = 4. What is the value of b? |
b = -8 |

Blake knows that one of the solutions to x2 – 6x + 8 = 0 is x = 2. What is the other solution? |
x = 4 |

An equation has solutions of m = -5 and m = 9. Which could be the equation? |
(m + 5)(m – 9) = 0 |

Which equations are true for x = -2 and x = 2? Check all that apply. |
a,d |

The roots of the function f(x) = x2 – 2x – 3 are shown. What is the missing number? x = -1 and x = ___ |
XX -3 |

Which function has zeros at x = 10 and x = 2? |
f(x) = x2 – 12x + 20 |

Which equation is true for x = -6 and x = 2? |
2×2 + 8x – 24 = 0 |

Which function has real zeros at x = 3 and x = 7? |
f(x) = x2 + 4x – 21 |

polynomial: |
an expression involving a sum of powers in one or more variables multiplied by coefficients, where the powers must be whole numbers |

viable : |
capable of working successfully; practical; realistic; usable; possible |

What are the solutions of the equation 4×2 + 3x = 24 – x? |
-3 or 2 |

Two negative integers are 5 units apart on the number line, and their product is 126. What is the sum of the two integers? |
-23 |

A rectangular piece of paper has a width that is 3 inches less than its length. It is cut in half along a diagonal to create two congruent right triangles with areas of 44 square inches. Which statements are true? Check all that apply. |
The area of the rectangle is 88 square inches. The equation x2 – 3x – 88 = 0 can be used to solve for the length of the rectangle. The triangle has a base of 11 inches and a height of 8 inches. |

Which is a solution to the equation? (x −2)(x + 5) = 18 |
x = −7 |

Which is a solution to (x − 2)(x + 10) = 13? |
x = 3 |

Which is a solution to (x – 3)(x + 9) = -27? |
x = 0 |

What is the only solution of 2×2 + 8x = x2 – 16? |
-4 |

John has 48 square centimeter tiles he wants to use to create a mosaic. He wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width. Which equation could John solve to find w, the greatest width in centimeters he can use for the mosaic? |
w(w + 2) = 48 |

Two factors of -48 have a difference of 19. The factor with a greater absolute value is positive. |
13 |

The product of two consecutive negative integers is 600. What is the value of the lesser integer? |
-25 |

A rectangle has an area of 40 square units. The length is 6 units greater than the width. |
10 by 4 |

Two negative integers are 8 units apart on the number line and have a product of 308. Which equation could be used to determine x, the smaller negative integer? |
x2 + 8x – 308 = 0 |

For what values of x is x2 + 2x = 24 true? |
4 and -6 |

Two positive integers are 3 units apart on a number line. Their product is 108. Which equation can be used to solve for m, the greater integer? |
XX m(m + 3) = 108 |

approximate: |
(verb) to come close to |

isolate: |
(verb) to separate from other substances; to place apart so as to be alone |

What are the solution(s) to the quadratic equation 50 – x2 = 0? |
x = ±5— 2 with a square root |

What are the solutions of the quadratic equation (x + 3)2 = 49? |
x = 4 and x = -10 |

Which are the roots of the quadratic function f(b) = b2 – 75? Check all that apply. |
b = 5 sr 3 b = -5 sr 3 |

What are the solution(s) to the quadratic equation 9×2 = 4? |
XX x = 3/2 and x = -3/2 |

What are the solutions to the quadratic equation x2 – 16 = 0? |
x = 4 and x = -4 |

Jillian is trying to save water, so she reduces the size of her square grass lawn by 8 feet on each side. The area of the smaller lawn is 144 square feet. In the equation What were the dimensions of the original lawn? |
XX 8 -6 sr 2feet by 8 + 6 sr 2 |

What is the first step in solving the quadratic equation x2 – 40 = 0? |
adding 40 to both sides of the equation |

What are the solution(s) to the quadratic equation x2 – 25 = 0? |
x = 5 and x = -5 |

Which are the roots of the quadratic function f(q) = q2 – 125? Check all that apply. |
XX q = 3 sr 5 q = -3 sr 5 |

Theo started to solve the quadratic equation (x + 2)2 – 9 = -5. He added 9 to both sides and the resulting equation was Which was the resulting equation of that step? |
x + 2 = ±2 |

Which statement is true about the quadratic equation 8×2 − 5x + 3 = 0? |
The leading coefficient is 8. |

Which shows the correct substitution of the values a, b, and c from the equation 0 = – 3×2 – 2x + 6 into the quadratic formula? |
a |

What is the value of the discriminant for the quadratic equation 0 = x + 2 + x2? |
-7 |

What is the value of the discriminant for the quadratic equation 0 = 2×2 + x – 3? |
25 |

The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown. Step 1: -c = ax2 + bx Which best explains or justifies Step 1? |
XX factoring out the constant |

What are the values of a, b, and c in the quadratic equation 0 = 1/2x^2 – 3x – 2? |
b |

Which shows the correct substitution of the values a, b, and c from the equation 1 = -2x + 3×2 + 1 into the quadratic formula? |
XX c |

Determine the discriminant for the quadratic equation 0 = -2×2 + 3. Based on the discriminant value, how many real number solutions does the equation have? Discriminant = b2 – 4ac _______real number solutions |
2 |

Which shows the correct substitution of the values a, b, and c from the equation 0 = 4×2 + 2x – 1 into the quadratic formula below? |
a |

Mattie uses the discriminant to determine the number of zeros the quadratic equation 0 = 3×2 – 7x + 4 has. Which best describes the discriminant and the number of zeros? |
The equation has no zeros because the discriminant is not a perfect square. |

A quadratic equation of the form 0 = ax2 + bx + c has a discriminant value of 0. How many real number solutions does the equation have? |
1 |

What is the discriminant of the quadratic equation 0 = -x2 + 4x – 2? |
8 |

What are the zeros of the function f(x) = x2 + 5x + 5 written in simplest radical form? |
c |

A quadratic equation of the form 0 = ax2 + bx + c has a discriminant value of -16. How many real number solutions does the equation have? |
0 |

Nathaniel is using the quadratic formula to solve 0 = x2 + 5x – 6. His steps are shown below. What are the solutions to the equation? |
x = -6, 1 |

Rhett is solving the quadratic equation 0= x2 – 2x – 3 using the quadratic formula. Which shows the correct substitution of the values a, b, and c into the quadratic formula? |
XX c |

In simplest radical form, what are the solutions to the quadratic equation 6 = x2 – 10x? |
x = 5 squ 31 |

A quadratic equation has exactly one real number solution. Which is the value of its discriminant? |
0 |

https://quizlet.com/83299681/solving-quadratic-equations-quadratic-formula-flash-cards/ |
… |

A computer company makes a rectangular screen with a diagonal of 20 inches. The width of the screen is 4 inches less than its length. The dimensions of the computer screen are modeled by the equation x2 + (x – 4)2 = 202. What is the value of x, the length of the screen? |
x=16 |

The product of two positive numbers is 750. The first number is 5 less than the second number. The equation What is the value of the greater number? |
30 |

The product of two consecutive positive integers is 812. What is the value of the lesser integer? |
28 |

The product of two numbers is 450. The first number is half the second number. Which equation can be used to find x, the greater number? |
1/2 x^2 = 450 |

he product of two positive numbers is 1,800. One number is twice the other number. The equation to determine the two numbers, with x representing the value of the lesser number, is x(2x) = 1,800. What is the value of the lesser number? |
30 |

A rocket is launched into the air. The projectile motion of the rocket can be modeled using h(t) = 112t -16t2, where t is the time since launch in seconds and h(t) is the height of the rocket at time t. When will the rocket be 196 feet in the air? |
… |

The projectile motion of an object can be modeled using A rocket is launched from the ground at an initial velocity of 39.2 meters per second. Which equation can be used to model the height of the rocket after t seconds? |
XX s(t) = -4.9t2 + 39.2t + 39.2 s(t) = -4.9t2 + 39.2 |

The product of two numbers is 713. The first number is 9 more than the second number. Which equation can be used to find x, the greater number? |
XX x(x + 9) = 713 |

Sergei buys a rectangular rug for his living room. He measures the diagonal of the rug to be 18 feet. The length of the rug is 3 feet longer than the width. What are the approximate dimensions of the rug? Round each dimension to the nearest tenth of a foot. |
14.1 feet by 11.1 feet |

A rectangle’s width is 2 meters shorter than its length, l. Its area is 168 square meters. Which equation can be used to find the length of the rectangle? |
l(l – 2) = 168 |

Kyla makes a triangular school pennant. The area of the triangle is 180 square inches. The base of the pennant is z inches long. The height is 6 inches longer than twice the base length. What is the height of the pennant? Recall the formula |
30 inches |

The product of two numbers is 240. The first number is 8 less than the second number. Which equation can be used to find x, the lesser number? |
XX x(x – 8) = 240 x2 – 8 = 240 |

The function g(x) is defined as g(x) = 6×2 + 23x – 4. When does g(x) = 0? |
x = -4 or x = 1/6 |

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? |
w(2w + 5) = 50 |

What are the solutions to m2 – 9 = 0? |
m = -3 and m = 3 |

The first step in solving the quadratic equation -5×2 + 8 = 133 is to subtract__ from each side. |
8 |

Mischa wrote the quadratic equation 0 = -x2 + 4x – 7 in standard form. What is the value of c in her equation? |
-7 |

Between which two ordered pairs does the graph of f(x) = 1/2x^2 + x – 9 cross the negative x-axis? |
(-6, 0) and (-5, 0) |

What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = −2×2 − 3x + 8, and what does it mean about the number of real solutions the equation has? |
The discriminant is 73, so the equation has 2 real solutions. |

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

What is a solution to (x + 6)(x + 2) = 60? |
x=4 |

What values of b satisfy 4(3b + 2)2 = 64? |
b =1/2 and b = -2 |

Which equation has an a-value of -2, a b-value of 1, and a c-value of 3? |
0 = -2×2 + x + 3 |

What is the value of the discriminant of the quadratic equation −2×2 = −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 one real number solution. |

Which function has real zeros at x = −10 and x = −6? |
f(x) = x2 + 16x + 60 |

Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = -6. Which function could Heather be writing? |
f(x) = -x2 – 12x – 36 |

Liliana decides to crop a square photo 2 inches on each side to fit it into a frame. The area of the original photo was 121 square inches. In the equation (x + 2)2 = 121, x represents the side measure of the cropped photo. What are the dimensions of the cropped photo? |
9 inches by 9 inches |

# Algebra- 4

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