Algebra Spring semester review 2025

• A. x = 1

• B. x = -1

• C. x = 2

• D. x = -2

Answer explanation

The Axis of Symmetry for a quadratic function g(x) = ax^2 + bx + c is given by the formula x = -b/(2a). Here, a = -3 and b = 6, so x = -6/(2*-3) = 1. Thus, the Axis of Symmetry is x = 1, which corresponds to choice A.

• (2, 1)

• (-2, -11)

• (2, -1)

• (-2, 1)

Answer explanation

To find the vertex of the quadratic function f(x) = -x^2 + 4x - 3, use the vertex formula x = -b/(2a). Here, a = -1 and b = 4, giving x = 2. Plugging x = 2 into f(x) gives f(2) = -1, so the vertex is (2, -1).

• Max 3

• Min 1

• Max 1

• Min 2

Answer explanation

The quadratic function f(x) = -x^2 + 4x - 3 opens downwards, indicating a maximum value. To find it, use the vertex formula x = -b/(2a). Here, a = -1 and b = 4, giving x = 2. Substituting x = 2 into f(x) yields f(2) = 1, so the max value is 1.

• (0, 5)

• (0, 6)

• (-3, 0)

• (0, 8)

Answer explanation

To find the y-intercept of the function g(x) = -3x^2 + 6x + 5, set x = 0. This gives g(0) = 5, so the y-intercept is (0, 5). Thus, the correct answer is (0, 5).

• (-∞, ∞)

• (-∞, 1]

• [1, ∞)

• (-∞, 2]

Answer explanation

The quadratic function g(x) = -x^2 + 4x - 3 opens downwards. Its vertex, found at x = 2, gives the maximum value g(2) = 1. Thus, the range is (-∞, 1], making the correct choice (-∞, 1].

• (3y - 7)(3y - 7)

• (3y - 7)(3y + 7)

• (9y - 49)(9y + 49)

• (3y - 49)(3y + 49)

Answer explanation

To factor 9y^2 - 49, recognize it as a difference of squares: (3y)^2 - 7^2. This factors to (3y - 7)(3y + 7), making it the correct choice.

• (x + 7)(x + 5)

• (x - 7)(x - 5)

• (x + 4)(x + 9)

• (x - 4)(x - 9)

Answer explanation

To factor x^2 + 12x + 35, we look for two numbers that multiply to 35 and add to 12. The numbers 7 and 5 fit this, so we can write the expression as (x + 7)(x + 5). Thus, the correct choice is (x + 7)(x + 5).

• {2, 5}

• {-2, -5}

• {-2, 5}

• {2, -5}

Answer explanation

To solve the equation x^2 - 7x + 10 = 0, we can factor it as (x - 2)(x - 5) = 0. Setting each factor to zero gives us the solutions x = 2 and x = 5. Thus, the correct answer is {2, 5}.

• {5 ± √6}

• {10 ± 21√2}

• {-5 ± 21√2}

• {-10 ± 21√2}

Answer explanation

To solve the equation x^2 - 10x + 19 = 0, we use the quadratic formula x = (10 ± √(10^2 - 4*1*19)) / (2*1). This simplifies to x = 5 ± √6, making {5 ± √6} the correct answer.

Simplify: √-50

• 5i√2

• 2i√25

• -7i

• i√100

Answer explanation

To simplify √-50, we recognize that √-1 = i. Thus, √-50 = √(25 * -2) = √25 * √-2 = 5i√2. Therefore, the correct answer is 5i√2.