Algebra Unit 3B Lesson 2
Between which two ordered pairs does the graph of f(x) = x2 + x - 9 cross the negative x-axis? Quadratic formula: x =
(-6, 0) and (-5, 0)
An equation has solutions of m = -5 and m = 9. Which could be the equation?
(m + 5)(m - 9) = 0
What is the only solution of 2x2 + 8x = x2 - 16?
-4
A quadratic equation has zero real number solutions. Which could be the discriminant value associated with this equation?
-5
What are the zeros of the quadratic function f(x)=2x2+16x-9
Not b
Solve x2 − 24x = −80 by completing the square. What is the solution set of the equation?
{4, 20}
Solve x2 + 14x = −24 by completing the square. What is the solution set of the equation?
{−12, −2}
A quadratic equation of the form 0 = ax2 + bx + c has one real number solution. Which could be the equation?
0 = -2x2 - 4x - 2
A quadratic equation has a discriminant of 12. Which could be the equation?
0 = 2x2 + 6x + 3
Ramiya is using the quadratic formula to solve a quadratic equation. Her equation is x = after substituting the values of a, b, and c into the formula. Which is Ramiya's quadratic equation? Quadratic formula: x =
0 = x2 + 3x + 2
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
Which are the roots of the quadratic function f(q) = q2 - 125? Check all that apply.
1 and 2
Patel is solving 8x2+16x+3=0 check all that apply
1,2,5
Sergey is solving 5x2 + 20x - 7 = 0. Which steps could he use to solve the quadratic equation? Check all that apply.
2,3,and4
Sienne is solving the quadratic equation by completing the square. What is the value of A.
3
What value of c makes x2 − 12x + c a perfect square trinomial?
36
Mariya is solving the quadratic equation by completing the square. 4x2 - 20x + 3 = 0 4x2 - 20x = -3 A(x2 - 5x) = -3 What is the value of A?
4
For what values of x is x2 + 2x = 24 true?
4 and -6
The first few steps in solving the quadratic equation 5x2 + 27x = 14 − 13x by completing the square are shown. 5x2 + 27x = 14 − 13x 5x2 + 40x = 14 5(x2 + 8x) = 14 Which is the best step to do next to solve the equation by completing the square?
5(x2 + 8x + 16) = 94
Atraeus is solving the quadratic equation by completing the square. 7x2 - 14x + 6 = 0 7x2 - 14x = -6 A(x2 - 2x) = -6 What is the value of A?
7
The function g(x) is defined as g(x) = 6x2 + 23x - 4. When does g(x) = 0?
B.
Sunil is solving the quadratic equation by completing the square. What should sunil do next.
C.
What are the solution(s) of the quadratic equation 98 - x2 = 0?
C.
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?
D.
Solve x2 = 12x - 15 by completing the square. Which is the solution set of the equation?
D.
Which are the solutions of x2 = -7x - 8?
D.
Which is the graph of a quadratic equation that has a negative discriminant?
D.
Which is a zero of the quadratic function f(x)=9x2-54x-19
Not b
In which step did tran first make an error.
Not d
What are the zeros of the quadratic function f(x)=6x2+12x-7
Not d
What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = −2x2 − 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.
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 one real number solution.
What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = x2 − 4x + 5, and what does it mean about the number of real solutions the equation has?
The discriminant is −4, so the equation has no real solutions
Anderson uses the discriminant to correctly find the number of real solutions of the quadratic equation x2 + 4x + 8 = 0. Which explanation could Anderson provide?
The equation has one real number solution because the discriminant is 0
What are the values of a, b, and c in the quadratic equation -2x2 + 4x - 3 = 0?
a = -2, b = 4, c = - 3
What are the values of a, b, and c in the quadratic equation 0 = 5x - 4x2 - 2?
a = -4, b = 5, c = -2
What are the values of a, b, and c in the quadratic equation 0 = x2 - 3x - 2?
a =1/2 , b = -3, c = -2
Which shows the correct substitution of the values a, b, and c from the equation 1 = -2x + 3x2 + 1 into the quadratic formula? Quadratic formula:
a.
The only solution of the equation x2 + bx + 16 = 0 is x = 4. What is the value of b?
b = -8
What are the zeros of the function f(x) = x2 + 5x + 5 written in simplest radical form? Quadratic formula: x =
c
What are the zeros of the quadratic function f(x) = 2x2 - 10x - 3?
c.
Some of the steps in the derivation of the quadratic formula are shown. Step 3: -c + = a Step 4a: -c + = a Step 4b: + = a Which best explains or justifies Step 4b?
converting to a common denominator
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
Which function has real zeros at x = −10 and x = −6?
f(x) = x2 + 16x + 60
Which function has zeros at x = 10 and x = 2?
f(x) = x2 - 12x + 20
Which function has zeros at x = −2 and x = 5?
f(x) = x2 − 3x − 10
What are the solutions to m2 - 9 = 0?
m = -3 and m = 3
Alessandro wrote the quadratic equation -6 = x2 + 4x - 1 in standard form. What is the value of c in his new equation?
not -1
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?
not 2 or 1
What is the discriminant of the quadratic equation 3 - 4x = -6x2?
not a
What is the value of the discriminant for the quadratic equation 0 = 2x2 + x - 3? Discriminant = b2 - 4ac
not a
What is the value of the discriminant for the quadratic equation -3 = -x2 + 2x? Discriminant = b2 - 4ac
not c
What is the value of the discriminant of the quadratic equation −1 = 5x2 −2x, and what does its value mean about the number of real number solutions the equation has?
not c
Which shows the correct substitution of the values a, b, and c from the equation -2 = -x + x2 - 4 into the quadratic formula? Quadratic formula: x =
not c
A quadratic equation has exactly one real number solution. Which is the value of its discriminant?
not c or d
Some of the steps in the derivation of the quadratic formula are shown. Step 4: Step 5: Step 6: Step 7: Which best explains why the expression cannot be rewritten as during the next step?
not d
Which shows the correct substitution of the values a, b, and c from the equation 1 = -2x + 3x2 + 1 into the quadratic formula? Quadratic formula:
not d
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
Theo started to solve the quadratic equation (x + 2)2 - 9 = -5. He added 9 to both sides and the resulting equation was (x + 2)2 = 4. Next, he took the square root of each side. Which was the resulting equation of that step?
x + 2 = ±2
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
What are the solutions to x2 + 8x + 7 = 0?
x = -7 and x = -1
Which is a solution to (x - 3)(x + 9) = -27?
x = 0
Which is a solution to the equation? (x − 3)(x − 5) = 35
x = 10
Which is a solution to (x − 2)(x + 10) = 13?
x = 3
Solve x2 - 8x = 20 by completing the square. Which is the solution set of the equation?
{-2, 10}
Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?
{-7, 1}
Determine the discriminant for the quadratic equation 0 = -2x2 + 3. Based on the discriminant value, how many real number solutions does the equation have? Discriminant = b2 - 4ac
2
The first few steps in solving the quadratic equation 8x2+80x=-5 by completing the square are shown.
200
Atraeus is solving the quadratic equation by completing the square. What is the value of A.
7
The first step in solving the quadratic equation -5x2 + 8 = 133 is to subtract from each side.
8
What is the discriminant of the quadratic equation 0 = -x2 + 4x - 2?
8
What value of c makes x2 + 6x + c a perfect square trinomial?
9
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
In which step did yvonne make a mistake.
A.
Solve x2 - 8x = 3 by completing the square. Which is the solution set of the equation?
A.
What are the solutions of 3x2 + 14x + 16 = 0?
A.
What are the solutions to the quadratic equation (5y + 6)2 = 24?
A.
What are the zeros of the quadratic function f(x) = 2x2 + 8x - 3?
A.
What should gio do first.
A.
What is a solution to (x + 6)(x + 2) = 60?
x = 4
What are the solutions of the quadratic equation (x + 3)2 = 49?
x = 4 and x = -10
What are the solutions to the quadratic equation x2 - 16 = 0?
x = 4 and x = -4
What are the solution(s) to the quadratic equation x2 - 25 = 0?
x = 5 and x = -5
What are the solutions to the quadratic equation 3(x − 4)2 = 75?
x = −1 and x = 9
What are the solutions to the equation? x2 + 6x = 40
x = −10 and x = 4
What are the solutions to the quadratic equation 4(x + 2)2 = 36
x = −5 and x = 1
Which is a solution to the equation? (x −2)(x + 5) = 18
x = −7
Which equations are true for x = -2 and x = 2? Check all that apply.
x2 - 4 = 0 4x2 = 16
Which are the roots of the quadratic function f(b) = b2 - 75? Check all that apply.
1and 2
Mischa wrote the quadratic equation 0 = -x2 + 4x - 7 in standard form. What is the value of c in her equation?
-7
What is the value of the discriminant for the quadratic equation 0 = x + 2 + x2? Discriminant = b2 - 4ac
-7
Isoke is solving the quadratic equation by completing the square. 10x2 + 40x - 13 = 0 10x2 + 40x = 13 A(x2 + 4x) = 13 What is the value of A?
10
Two factors of -48 have a difference of 19. The factor with a greater absolute value is positive. What is the sum of the factors?
13
What value of c makes x2 − 24x + c a perfect square trinomial?
144
Lie is solving a quadratic equation by completing the square. What should lie do next
B.
What are the zeros of the quadratic function f(x)=16x2+32x-9
B.
Which are the solutions of x2 = 19x + 1?
B.
What are the zeros of the quadratic function f(x)=2x2-10x-3
C
What should maya do first
C.
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?
subtraction property of equality
Mattie uses the discriminant to determine the number of zeros the quadratic equation 0 = 3x2 - 7x + 4 has. Which best describes the discriminant and the number of zeros?
The equation has two zeros because the discriminant is greater than 0.
Which statement is true about the quadratic equation 8x2 − 5x + 3 = 0?
The leading coefficient is 8.
A student is deriving the quadratic formula. Her first two steps are shown. Step 1: -c = ax2 + bx Step 2: Which best explains or justifies Step 2?
factoring the binomial
Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is -99. Which equation can be used to find m, the midpoint of the two numbers?
m2 - 100 = -99
Zacharias is using the quadratic formula to solve the equation 0 = -2x2 + 5x - 3. He begins by substituting as shown. Quadratic formula: x = Substitution: x = What error did Zacharias make?
not a
In simplest radical form, what are the solutions to the quadratic equation 0 = -3x2 - 4x + 5? Quadratic formula: x =
not b
What is the positive solution to the equation 0 = -x2 + 2x + 1? Quadratic formula: x =
not b
Quincy uses the quadratic formula to solve for the values of x in a quadratic equation. He finds the solution, in simplest radical form, to be x = . Which best describes how many real number solutions the equation has?
not b or c
What is the discriminant of the quadratic equation 0 = 2x2 + 3x - 5?
not b or c
In simplest radical form, what are the solutions to the quadratic equation 6 = x2 - 10x? Quadratic formula: x =
not c
What is the discriminant of the quadratic equation 0 = 2x2 + 3x - 5?
not c
Which shows the correct substitution of the values a, b, and c from the equation 0 = - 3x2 - 2x + 6 into the quadratic formula? Quadratic formula: x =
not c or b