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# Questions on Quadratics Trivia Quiz

### Quadratic equations and the formula used to attain the correct answers are certainly wonderful. On the other hand many would be delighted if they never saw a quadratic again. Well...sorry! Enjoy!

A multiple-choice quiz by jonnowales. Estimated time: 3 mins.

Author
Time
3 mins
Type
Multiple Choice
Quiz #
272,401
Updated
May 20 24
# Qns
10
Difficulty
Average
Avg Score
8 / 10
Plays
9498
Awards
Top 10% Quiz
Last 3 plays: granpa46 (8/10), Guest 71 (2/10), psnz (10/10).
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Question 1 of 10
1. When given a relatively basic quadratic question such as x^2 + 9x + 20, which of these options is a suitable way to solve it? Hint

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Question 2 of 10
2. What would be the two constituents of the following quadratic question: x^2 + x - 6? Hint

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Question 3 of 10
3. Basic arithmetic will be important in your attempt to solve the next question. What are the two constituents of x^2 - 9x + 18?
Hint

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Question 4 of 10
4. Quadratics are not always basic and often the x^2 term will have a co-efficient greater than 1. What are the two components of the following: 3x^2 + 9x + 6? (There are other possibilities, however, only one of the following answers is correct) Hint

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Question 5 of 10
5. An equation is a phrase which contains an equals (=) sign and is therefore able to be solved to give roots (answers). In quadratics there are two answers (which may, however be imaginary, complex or identical). Solve the following equation: x^2 - 4x + 4 = 0. Hint

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Question 6 of 10
6. Solve the following quadratic equation: x^2 + 2x - 8 = 0. Hint

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Question 7 of 10
7. In those dreaded maths examinations, students are often given the components and are asked to find the original quadratic expression. Find the expression from the following constituents: (x+8) and (x-3).
Hint

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Question 8 of 10
8. Find the expression from the given components: (x-6) and (x-4). Hint

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Question 9 of 10
9. The topic of quadratics does indeed have an equation, and boy is it an equation! X = -b ± (?) / 2a. Within this equation you will see a missing portion indicated by a question mark in brackets/parentheses. (?) = the square root of what? Hint

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Question 10 of 10
10. Quadratic equations can also be shown graphically. If the quadratic expression was positive: y = 3x^2 + x - 2, what shape would the graphical curve be? Hint

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Quiz Answer Key and Fun Facts
1. When given a relatively basic quadratic question such as x^2 + 9x + 20, which of these options is a suitable way to solve it?

Factorising is a way of splitting up the original equation into, as the name suggests, factors or constituents. In the example given, x^2 + 9x + 20 (^ meaning to the power of), the factors would be (x+4) and (x+5).
If you use the method of FOIL (First, Inner, Outer, Last) to multiply these two factors you will see that you will go back to the original equation.

(x+4)(x+5) - x multiplied by x is (x^2), 4 multiplied by x is (4x), 5 multiplied by x is (5x) and 4 multiplied by 5 is (20). As you can see, the answers in the brackets are the components of my original quadratic equation.
2. What would be the two constituents of the following quadratic question: x^2 + x - 6?

The answer is (x+3) (x-2) and here is the proof. Using the method of FOIL - x multiplied by x is (x^2), 3 multiplied by x is (3x), -2 multiplied by x is (-2x) and 3 multiplied by -2 is (-6). So, you are left with the equation x^2 + 3x - 2x - 6. This can be further simplified by using basic algebra as 3x - 2x equals 1x (the co-efficient of x which is one, is pretty redundant in this case and is therefore simply expressed as just x).
3. Basic arithmetic will be important in your attempt to solve the next question. What are the two constituents of x^2 - 9x + 18?

The common mistake made in this sort of equation where the co-efficient of x is negative whilst the number on its own is positive is the multiplication of two negative numbers. One of the fundamental rules of arithmetic is that a negative multiplied by a negative equates to a positive.
4. Quadratics are not always basic and often the x^2 term will have a co-efficient greater than 1. What are the two components of the following: 3x^2 + 9x + 6? (There are other possibilities, however, only one of the following answers is correct)

These are slightly more difficult to solve. There are various methods available such as cross multiplication and so on. However, the method I am going to use to explain this is quicker as you don't have to go by trial and error to attain your roots (answers).

The original equation was 3x^2 + 9x + 6. Quadratic questions follow a general rule which is ax^2 + bx + c. This indicates that x^2 is component a, the x term is component b and the stand alone number is component c.
The first step would be to multiply the co-efficient of component a and component c together which would equal, in this instance, 18 (3 x 6). The next step would be to find two numbers that multiply together to make that total of 18 and also add together to the sum of the co-efficient of the component b which, in this instance is equal to 9. The only two numbers able to do so are 6 and 3. So, you now split component b (9x) into the two new co-efficient which are 6 and 3 (6x + 3x). Your new formula is 3x^2 + 6x + 3x + 6. The next step would be to factorise this equation in pairs, 3x^2 + 6x and 3x + 6. If we take 3x^2 + 6x, we need to find the highest common factor which, in this case, is 3x. If you divide 3x^2 and 6x by 3x you get 3x(x+2). If we then take the second half which is 3x + 6, you will find that the highest common factor is 3. Divide both 3x and 6 by 3 and you get 3(x+2). If we put both of these factors together we get 3x(x+2) + 3(x+2). You will notice that both terms inside the brackets/parentheses are x+2 - this is a clear indication that you are on course for the correct answer. You now group the terms outside the brackets and the terms inside the brackets together. You will get (3x+3) and (x+2), et voila, it matches the answer given.

This seems like a long winded and drawn out process, but, with a bit of practice it is possible to solve the problem within 30 seconds.
5. An equation is a phrase which contains an equals (=) sign and is therefore able to be solved to give roots (answers). In quadratics there are two answers (which may, however be imaginary, complex or identical). Solve the following equation: x^2 - 4x + 4 = 0.

Answer: x = 2, x = 2

The first stage of this equation is factorisation. You are looking for two numbers that multiply to give 4 and add to give -4. After a bit of mental arithmetic you should come up with -2 and -2 as -2 + -2 = -4 and -2 x -2 = 4. As this is an equation the following step is to solve the equation to attain the roots: x - 2 = 0 and x - 2 = 0. Using basic algebra, you add two to each side of the equations and you come up with the answers x = 2 and x = 2. Yes, these answers are the same -- x = 2 is a double root.
6. Solve the following quadratic equation: x^2 + 2x - 8 = 0.

Answer: x = -4, x = 2

The first step is factorisation. What two numbers add together to make 2 and multiply together to produce -8. After that dreaded mental arithmetic you arrive at the terms (x+4) and (x-2). As the equation states the components add up to a total of zero, you reach the following: x + 4 = 0 and x - 2 = 0. Basic algebra attains the answers x = -4 and x = 2.
7. In those dreaded maths examinations, students are often given the components and are asked to find the original quadratic expression. Find the expression from the following constituents: (x+8) and (x-3).

Answer: x^2 + 5x - 24

FOIL (First, Inner, Outer, Last) is a very good mnemonic for remembering how to expand brackets/parentheses. (x+8)(x-3): x multiplied by x = (x^2), 8 multiplied by x = (8x), -3 multiplied by x = (-3x) and 8 multiplied by -3 = (-24).
Put these together and you get: x^2 + 8x - 3x - 24. This can be simplified to make: x^2 + 5x - 24.
8. Find the expression from the given components: (x-6) and (x-4).

Answer: x^2 - 10x + 24

This one can be a little tricky especially when you are doing the 'last' stage of FOIL. First: x multiplied by x = (x^2). Outer: -4 multiplied by x = (-4x). Inner: -6 multiplied by x = (-6x). Last: -6 multiplied by -4 = (24). NOT -24!
Put all of these together and you get x^2 - 4x - 6x + 24. Simplify and you get x^2 - 10x + 24.
9. The topic of quadratics does indeed have an equation, and boy is it an equation! X = -b ± (?) / 2a. Within this equation you will see a missing portion indicated by a question mark in brackets/parentheses. (?) = the square root of what?

The full equation is x = (-b ± [square root b^2 - 4ac]) / 2a. Quite a mouthful, however, if known by heart makes the topic of quadratics a lot easier! Bearing in mind that quadratic expressions follow the pattern ax^2 + bx + c = 0, the quadratic formula is just a device to substitute the letters (a, b and c) with numbers given in the expression. If the equation is, for instance, (1)x^2 + 5x + 6: a = 1, b = 5 and c = 6. Simply substitute the letters for those numbers and the rest is basic arithmetic.
10. Quadratic equations can also be shown graphically. If the quadratic expression was positive: y = 3x^2 + x - 2, what shape would the graphical curve be?

If the quadratic expression is positive (indicated by the co-efficient of x^2 being positive) then a 'u' shaped curve will be given. This is known as a parabola. If the quadratic expression is negative (indicated by the co-efficient of x^2 being negative) then an 'n' shaped curve will be given.

Thanks for playing this quiz - if your head is hurting, you are not alone! Hope you enjoyed.
Source: Author jonnowales

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