Quiz about Solving Quadratic Equations Study Guide

Question 1

If the discriminant equals 0, then the quadratic has:

Accepted Answer

Real Solution

Answer

Real Solutions

Answer

Half a Solution

Answer

No Real Solution

Question 2

If the discriminant is negative, then the quadratic has:

Accepted Answer

No Real Solutions

Answer

Real Solution

Answer

Real Solutions

Answer

Half a Solution

Question 3

If the discriminant is positive, then the quadratic has:

Accepted Answer

Real Solutions

Answer

Real Solution

Answer

Half a Solution

Answer

No Real Solution

Question 4

Convert x²+6x+9 to factored form and identify the solution.

Accepted Answer

(x+3)(x+3); x=-3

Answer

(x+4)(x+5); x=-4, -5

Answer

(x-3)(x-3); x=3

Answer

Not factorable

Question 5

Factor x²-6x-40

Accepted Answer

(x-10)(x+4)

Answer

(x+10)(x-4)

Answer

(x-8)(x+5)

Answer

(x+8)(x-5)

Question 6

ax²+bx+c=0 is the standard form of a quadratic equation.

Accepted Answer

True

Answer

False

Question 7

The quadratic equation can be used to solve quadratic equations that cannot be factored.

Accepted Answer

True

Answer

False

Question 8

If Beauford wanted to solve this equation using factoring by grouping, which answer shows the correct sequence of steps? $$2x^2-5x-18=0$$

Accepted Answer

Multiply 2 and -18 together and factor -36 into -9 and 4.

Split -5x into -9x and +4x. Factor out the GCF from both groups, and factor out the GCF from both terms.

Set both factors equal to 0 and solve for x.

Answer

Multiply 2 and -18 together and factor -36 into -9 and 4.

Write the equation in factored form. Set the factors equal to 0 and solve for x.

Answer

Multiply 2 and -18 together and factor -36 into -9 and 4.

Split -5x into -9x and +4x. Factor out the GCF from both groups.

Set both terms equal to 0 and solve for x.

Answer

Factor 18 into -9 and 2

Write the equation in factored form. Set the factors equal to 0 and solve for x.

Question 9

If Carly wanted to solve the equation below by using the quadratic formula, which answer shows the correct sequence of steps?

Accepted Answer

Identify a=1, b=-12, and c=4.
Plug in the numbers for a, b, and c. Simplify the radical (square root sign). Simplify the numerator and divide by the denominator.

Answer

Identify a=1, b=-12, and c=4.
Plug in the numbers for a, b, and c. Simplify the radical (square root sign). Simplify the numerator.

Answer

Identify a=1, b=-12, and c=4.
Plug in the numbers for a, b, and c. Simplify the radical (square root sign).

Answer

This trinomial cannot be solved by the quadratic formula.

Question 10

If Delia wanted to solve the equation below by completing the square, which answer shows the correct sequence of steps? $$x^2-6x+4=0$$

Accepted Answer

Isolate the constant c value, find $$\left(\frac{-6}{2}\right)^2$$ , add 9 to both sides, factor the trinomial, then square root both sides and simplify.

Answer

Find $$\left(\frac{-6}{2}\right)^2$$ , add 9 to both sides, factor the trinomial, then square root both sides and simplify.

Answer

Isolate the constant c value, find $$\left(\frac{-6}{2}\right)^2$$ , add -3 to both sides, factor the trinomial, then square root both sides and simplify.

Answer

This trinomial cannot be solved by completing the square.

Question 11

What are the x-intercepts of the graph of -4x²+25x+21 = 0?

Accepted Answer

x = -3/4, 7

Answer

x = -7, -3/4

Answer

x = -7, 3/4

Answer

x = 3/4, 7

Question 12

If Alucard wanted to solve this equation using the square root method, which answer shows the correct sequence of steps? $$x^2-41=8$$

Accepted Answer

Add 41 to both sides, then square root both sides.

Answer

Take the square root of both sides.

Answer

Subtract 41 from both sides, then square root both sides.

Answer

Subtract 8 from both sides, then square root both sides.

Solving Quadratic Equations Study Guide

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