Quadratic Equation Quiz
Questions: 16 · 10 minutes
1. Rewrite 3x^2 - 7 = 2x in standard form ax^2 + bx + c = 0.
3x^2 - 2x + 7 = 0, with the constant sign changed
3x^2 + 2x - 7 = 0, with 2x moved using the wrong sign
3x^2 - 2x - 7 = 0, after subtracting 2x from both sides
3x^2 - 9x = 0, after incorrectly combining unlike terms
2. A rectangle has width x metres, length x + 3 metres, and area 40 square metres. What is its width?
10 metres, found by treating the area as a perimeter
8 metres, which would make the area 88 square metres
4 metres, which would make the area 28 square metres
5 metres, since 5(5 + 3) = 40
3. A monic quadratic has roots -2 and 5. Which equation represents it?
x^2 + 3x - 10 = 0, which has the wrong sum of roots
x^2 - 3x - 10 = 0, obtained from (x + 2)(x - 5) = 0
x^2 - 7x + 10 = 0, which represents roots 2 and 5
x^2 + 3x + 10 = 0, which uses the wrong constant sign
4. Which equation has no real solutions?
x^2 - 6x + 9 = 0, whose discriminant equals zero
x^2 - 5x + 4 = 0, whose discriminant is positive
x^2 + 2x + 5 = 0, whose discriminant is negative
x^2 - 4 = 0, which is a difference of two squares
5. Which pair satisfies x^2 - 5x + 6 = 0?
The pair -2 and -3, whose sum is -5
The pair 2 and 3, which makes (x - 2)(x - 3) equal to zero
The pair 1 and 6, which has the right product but the wrong sum
The pair -1 and -6, which gives neither the required sum nor signs
6. The graph y = x^2 - 4x + 3 is symmetric about a vertical line through its vertex. What is that line?
x = 2, found from x = -b/(2a)
x = -2, from using b/(2a) instead
x = 4, from using the magnitude of the linear coefficient
x = -4, from using the signed linear coefficient directly
7. What does the discriminant reveal about x^2 + 4x + 8 = 0?
The discriminant is negative, so there are no real solutions.
The discriminant is zero, so there is one repeated real solution.
The discriminant is positive, so there are two distinct real solutions.
The discriminant directly gives the real solutions -4 and -8.
8. For which value of k does x^2 + 6x + k = 0 have one repeated real solution?
k = 3, obtained by halving the coefficient of x
k = 6, copied directly from the coefficient of x
k = 9, because the quadratic becomes (x + 3)^2 = 0
k = 36, obtained by squaring 6 without dividing first
9. Which factorization expands to 2x^2 + 7x + 3?
(2x + 3)(x + 1), which has a middle term of 5x
(2x + 1)(x + 3), which has a middle term of 7x
(2x - 1)(x - 3), which has a positive constant but negative middle term
(x + 1)(x + 3), which has leading coefficient 1 rather than 2
10. Where does the graph y = (x - 1)(x + 4) cross the x-axis?
At x = -1 and x = 4, after reversing both factor signs incorrectly
At x = 1 and x = 4, after reversing only the second factor sign
At x = -1 and x = -4, after reversing only the first factor sign
At x = 1 and x = -4, where each factor equals zero
11. A student writes 2x^2 + 3x - 2 as (2x - 1)(x + 2). Which conclusion is correct?
The factorization is correct, so the solutions are x = 1/2 and x = -2.
Both signs must be reversed, giving solutions x = -1/2 and x = 2.
Only the second factor is wrong; it should be x - 2, giving x = 1/2 and x = 2.
The quadratic cannot be factored using integer constants, so the formula is required.
12. Which expression correctly applies the quadratic formula to 3x^2 - 4x - 2 = 0?
x = (-4 ± sqrt(40)) / 6, using b instead of -b in the numerator
x = (4 ± sqrt(40)) / 6, using a = 3, b = -4, and c = -2
x = (4 ± sqrt(8)) / 3, with both the discriminant and denominator incorrect
x = (-4 ± sqrt(8)) / 3, without applying either sign rule correctly
13. After completing the square, which equation is equivalent to x^2 - 8x + 7 = 0?
(x - 4)^2 = 7, which does not account for the added 16 correctly
(x + 4)^2 = 9, which uses the wrong sign inside the square
(x - 4)^2 = 9, obtained by rewriting x^2 - 8x as (x - 4)^2 - 16
(x - 8)^2 = 57, which uses the full linear coefficient inside the square
14. What are the exact solutions of x^2 + 4x - 1 = 0?
x = 2 ± sqrt(5), with the sign of -b reversed incorrectly
x = -4 ± sqrt(5), without dividing the linear coefficient by 2
x = -2 ± sqrt(3), from an incorrect discriminant calculation
x = -2 ± sqrt(5), obtained by simplifying (-4 ± sqrt(20)) / 2
15. Solve x^2 = 16 over the real numbers.
x = 8 only, from doubling 4
x = 4 only, omitting the negative square root
x = 8 or x = -8, using twice the required magnitude
x = 4 or x = -4, since both values square to 16
16. Which completed-square form is equivalent to x^2 + 6x + 5?
(x + 3)^2 - 4, because expanding gives x^2 + 6x + 5
(x - 3)^2 - 4, which produces a middle term of -6x
(x + 6)^2 - 31, which produces a middle term of 12x
(x + 3)^2 + 4, which gives a constant term of 13