
The Quadratic Formula (Math Masters)
Authored by Ben Nguyen
Mathematics
8th Grade
CCSS covered

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15 questions
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1.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
What is the quadratic formula?
x=(-a±√(b²-4ac))/(2b)
x=(-b±√(b²-4ac))/(2a)
x=(b±√(b²+4ac))/(2a)
x=(b²-4ac)/(2a)
Answer explanation
The quadratic formula is used to find the roots of a quadratic equation. The correct formula is x=(-b±√(b²-4ac))/(2a), which allows for calculating the values of x based on coefficients a, b, and c.
Tags
CCSS.HSA-REI.B.4B
2.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
What does the term b²-4ac represent in the quadratic formula?
The vertex of a quadratic equation.
The slope of a linear equation.
The root of a polynomial function.
The discriminant of a quadratic equation.
Answer explanation
The term b²-4ac is known as the discriminant of a quadratic equation. It determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.
Tags
CCSS.HSA-REI.B.4B
3.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
If the discriminant is positive, how many real solutions does the quadratic equation have?
1 real solution
No real solutions
Infinite real solutions
2 real solutions
Answer explanation
If the discriminant of a quadratic equation is positive, it indicates that there are two distinct real solutions. Therefore, the correct answer is 2 real solutions.
Tags
CCSS.HSA-REI.B.4B
4.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
For the quadratic equation 2x2+4x+2=0, what are the values for a,b, and c?
a = 2, b = 4, c = 2
a = 3, b = 4, c = 1
a = 2, b = 2, c = 4
a = 1, b = 2, c = 3
Answer explanation
In the quadratic equation 2x² + 4x + 2 = 0, the coefficients are identified as a = 2, b = 4, and c = 2. Therefore, the correct choice is a = 2, b = 4, c = 2.
5.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
What is the discriminant for the equation x2-6x+9=0?
0
-1
4
6
Answer explanation
The discriminant is calculated using the formula b² - 4ac. For the equation x² - 6x + 9, a = 1, b = -6, and c = 9. Thus, the discriminant is (-6)² - 4(1)(9) = 36 - 36 = 0. Therefore, the correct answer is 0.
Tags
CCSS.HSA-REI.B.4B
6.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
How many real solutions does the equation x2+4x+5=0 have?
1
2
3
None
Answer explanation
The equation x² + 4x + 5 can be analyzed using the discriminant (b² - 4ac). Here, a=1, b=4, c=5. The discriminant is 4² - 4(1)(5) = 16 - 20 = -4, which is negative. Therefore, there are no real solutions.
Tags
CCSS.HSA-REI.B.4B
7.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Using the quadratic formula, what are the solutions for x2-2x-3=0?
x = 3, x = -1
x = 0, x = 4
x = 1, x = 3
x = 2, x = -3
Answer explanation
To solve x² - 2x - 3 = 0 using the quadratic formula x = (-b ± √(b² - 4ac)) / 2a, where a=1, b=-2, c=-3. This gives x = (2 ± √(4 + 12)) / 2 = (2 ± 4) / 2. Thus, x = 3 and x = -1 are the solutions.
Tags
CCSS.HSA-REI.B.4B
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