Algebra I - Unit 9: Quadratic Equations

Which equation results from taking the square root of both sides of (x - 9)2 = 81?

x - 9 + +-9

What is the solution to 2x^2+8x=x^2-16?

x = -4

What are the solutions to x^2 + 8x + 7 = 0?

x = -7 and x = -1

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

x = 4 and x = -10

A group of students is given a 10 by 10 grid to cut into individual unit squares. The challenge is to create two squares using all of the unit squares. Their teacher states that after the two new squares are formed, one should have a side length two units greater than the other. Which equation represents x, the side length of the greater square?

x^2 + (x - 2)^2 = 100

The sum of a number and its square is 42. Which equation can be used to find the two numbers for which this is true?

x^2 + x = 42

Which represents the solution(s) of the system of equations, y = x2 - x + 1 and y = x? Determine the solution set by graphing.

(1, 1)

Which represents the solution(s) of the graphed system of equations, y = -x2 + x + 2 and y = -x + 3?

(1, 2)

Brianna is graphing the function f(x) = x2 + 6x + 5. What x-intercepts should Brianna use to graph f(x)?

-5 and -1

Rounded to the nearest hundredth, what is the positive solution to the quadratic equation 0=2x^2+3x-8?

1.39

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

A rectangle has an area of 40 square units. The length is 6 units greater than the width. What are the dimensions of the rectangle?

10 by 4

What number should be added to both sides of the equation to complete the square? x^2 - 10x = 7

25

What number should be added to both sides of the equation to complete the square? x^2 + 12x = 11

36

A rectangle's length is three times its width, w. Its area is 243 square units. Which equation can be used to find the width of the rectangle?

3w^2 = 243

Zacharias is using the quadratic formula to solve the equation 0 = -2x2 + 5x - 3. He begins by substituting as shown. Substitution: x = -5 +- sq.r(5^2-4(2)(-3)) / 2(-2) What error did Zacharias make?

The 2 in the numerator should be -2.

The area of the right triangle shown is 24 square feet. Image ID: A right-triangle in which the hypotenuse equals 10ft, the first leg equals (x + 2)ft, and the last leg equal xft; there is also a note 'Not drawn to scale' Which equations can be used to find the lengths of the legs of the triangle?

[A] 0.5(x)(x + 2) = 24 [D] x^2 + 2x - 48 = 0 [E] x^2 + (x + 2)^2 = 100

Which equations are true for x = -2 and x = 2?

[A] x^2 - 4 = 0 [D] 4x^2 = 16

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

[C] c = +-7 sq.r(2)

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

[C] x = 5/2 - sq.r(31)/2 and x = 5/2 + sq.r(31)/2

Which shows the correct substitution of the values a, b, and c from the equation -2 = -x + x2 - 4 into the quadratic formula?

[D] x = -(-1) +- sq.root((-1)^2-4(1)(-2)) / 2(1)

Solve x^2 = 12x - 15 by completing the square. Which is the solution set of the equation?

[D] {6 - sq.root(21) , 6 + sq.root(21)}

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

c=5

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

Which represents the solution(s) of the graphed system of equations, y = x2 - 2x and y = -2x - 1?

no solutions