Algebra 1

What are the solutions of 3x2 + 14x + 16 = 0?

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

Which function has zeros at x = −2 and x = 5?

An equation has solutions of m = -5 and m = 9. Which could be the equation?

What are the solutions to x2 + 8x + 7 = 0?

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

Which function has zeros at x = 10 and x = 2?

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?

For what values of x is x2 + 2x = 24 true?

What is the only solution of 2x2 + 8x = x2 - 16?

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

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

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

What are the solutions to the equation? x2 + 6x = 40

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?

What are the solutions to the quadratic equation x2 - 16 = 0?

What are the solutions to the quadratic equation 3(x − 4)2 = 75?

What are the solutions of the quadratic equation (x + 3)2 = 49?

What are the solution(s) to the quadratic equation x2 - 25 = 0?

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

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?

Which are the roots of the quadratic function f(q) = q2 - 125? Check all that apply.

What are the solution(s) of the quadratic equation 98 - x2 = 0?

What are the solutions to the quadratic equation (5y + 6)2 = 24?

What value of c makes x2 − 24x + c a perfect square trinomial?

Solve x2 + 14x = −24 by completing the square. What is the solution set of the equation?

Solve x2 - 8x = 3 by completing the square. Which is the solution set of the equation?

Which are the solutions of x2 = 19x + 1?

What value of c makes x2 − 12x + c a perfect square trinomial?

Solve x2 = 12x - 15 by completing the square. Which is the solution set of the equation?

What value of c makes x2 + 6x + c a perfect square trinomial?

Which are the solutions of x2 = -7x - 8?

Atraeus is solving the quadratic equation by completing the square. What is the value of A.

What are the zeros of the quadratic function f(x)=2x2-10x-3

Sienne is solving the quadratic equation by completing the square. What is the value of A.

Patel is solving 8x2+16x+3=0 check all that apply

The first few steps in solving the quadratic equation 8x2+80x=-5 by completing the square are shown.

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?

What are the zeros of the quadratic function f(x) = 2x2 - 10x - 3?

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?

Sunil is solving the quadratic equation by completing the square. What should sunil do next.

What are the zeros of the quadratic function f(x)=2x2+16x-9

What are the zeros of the quadratic function f(x)=6x2+12x-7

What are the zeros of the quadratic function f(x)=16x2+32x-9

Lie is solving a quadratic equation by completing the square. What should lie do next

Which is a zero of the quadratic function f(x)=9x2-54x-19

In which step did yvonne make a mistake.

In which step did tran first make an error.

What should gio do first.

What should maya do first

Which statement is true about the quadratic equation 8x2 − 5x + 3 = 0?

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

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?

What are the values of a, b, and c in the quadratic equation -2x2 + 4x - 3 = 0?

What is the value of the discriminant for the quadratic equation -3 = -x2 + 2x? Discriminant = b2 - 4ac

What are the values of a, b, and c in the quadratic equation 0 = 5x - 4x2 - 2?

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 =

What is the value of the discriminant for the quadratic equation 0 = 2x2 + x - 3? Discriminant = b2 - 4ac

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:

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?

What is the value of the discriminant for the quadratic equation 0 = x + 2 + x2? Discriminant = b2 - 4ac

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 =

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?

Alessandro wrote the quadratic equation -6 = x2 + 4x - 1 in standard form. What is the value of c in his new equation?

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?

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:

What are the values of a, b, and c in the quadratic equation 0 = x2 - 3x - 2?

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?

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?

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?

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?

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 =

What is the discriminant of the quadratic equation 3 - 4x = -6x2?

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?

In simplest radical form, what are the solutions to the quadratic equation 6 = x2 - 10x? Quadratic formula: x =

What is the discriminant of the quadratic equation 0 = 2x2 + 3x - 5?

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

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?

A quadratic equation has a discriminant of 12. Which could be the equation?

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

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

In simplest radical form, what are the solutions to the quadratic equation 0 = -3x2 - 4x + 5? Quadratic formula: x =

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

What is the discriminant of the quadratic equation 0 = 2x2 + 3x - 5?

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?

What is the positive solution to the equation 0 = -x2 + 2x + 1? Quadratic formula: x =

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?

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?

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

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

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

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

What are the zeros of the quadratic function f(x) = 2x2 + 8x - 3?

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?

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?

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

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?

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

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?

The first step in solving the quadratic equation -5x2 + 8 = 133 is to subtract from each side.

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?

Which is a solution to the equation? (x − 3)(x − 5) = 35

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

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

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

What are the solutions to m2 - 9 = 0?

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

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?

A quadratic equation has zero real number solutions. Which could be the discriminant value associated with this equation?

Between which two ordered pairs does the graph of f(x) = x2 + x - 9 cross the negative x-axis? Quadratic formula: x =

Sergey is solving 5x2 + 20x - 7 = 0. Which steps could he use to solve the quadratic equation? Check all that apply.

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?