Algebra 1 B final assessment

What is the term classification of the following polynomial?
x³-7x²+3

• monomial

• binomial

• trinomial

• expression

Answer explanation

The polynomial x³ - 7x² + 3 has three terms: x³, -7x², and 3. Since it contains three distinct terms, it is classified as a trinomial.

Find the difference
(2x²-2x+3) - (3x²+4x-5)

• 7x - 7x + 5x²

• -x² - 6x -2

• -x² - 6x +8

• x² + 6x + 8

Answer explanation

To find the sum, distribute the negative sign: (3 - 2x + 2x²) - (4x - 5 + 3x²) = 3 - 2x + 2x² - 4x + 5 - 3x². Combine like terms: (2x² - 3x²) + (-2x - 4x) + (3 + 5) = -x² - 6x + 8. Thus, the correct answer is -x² - 6x + 8.

Tags

CCSS.HSA.APR.A.1

(2x +8y)(x + 4y)

• 2x² + 16yx + 32y²

• 2x² + 8yx + 32y²

• 2x² - 16yx + 32y²

• 2x² + +8x + 32

Answer explanation

To expand (2x + 8y)(x + 4y), use the distributive property: 2x*x + 2x*4y + 8y*x + 8y*4y = 2x^2 + 8xy + 8xy + 32y^2 = 2x^2 + 16xy + 32y^2. Thus, the correct answer is 2x^2 + 16yx + 32y^2.

Tags

CCSS.HSA.APR.A.1

Answer explanation

The function g(x) = (x + 4)² represents a horizontal shift of f(x) = x². The +4 indicates a shift 4 units to the left on the x-axis, transforming the graph accordingly.

Tags

CCSS.HSF-BF.A.1B

Factor
n² + 16n + 63

• (n-7)(n+4)

• (n+7)(n-9)

• (n-3)(n-10)

• (n+7)(n+9)

Answer explanation

To factor n² + 16n + 63, we look for two numbers that multiply to 63 and add to 16. The numbers 7 and 9 fit this, so we can write it as (n+7)(n+9). Thus, the correct answer is (n+7)(n+9).

What is the Quadratic Formula?

Answer explanation

The graph represents a quadratic function with a vertex. The correct choice, h(x)=x^2-6x, has its vertex at (3,-9), indicating a downward opening parabola, which matches the graph's characteristics.

Tags

CCSS.HSA-REI.B.4B

• left: 1, up: 4

• left: 1, down: 4

• right: 1, up: 4

• right: 4, up: 1

Answer explanation

The expression \( (x+1)^2 - 4 \) represents a transformation of the parent function \( x^2 \). The term \( (x+1) \) shifts the graph left by 1, and the \( -4 \) shifts it down by 4, making the correct choice: left: 1, down: 4.

• Vertex: (4,1)

• Vertex: (-4, -1)

• Vertex: (4, -1)

• Vertex: (-4, 1)

Answer explanation

The equation is in vertex form, y = a(x-h)^2 + k, where (h, k) is the vertex. Here, h = 4 and k = 1, so the vertex is (4, 1). Thus, the correct answer is Vertex: (4,1).

Convert the equation y= x² + 4x + 11 into vertex form.

• y = (x + 2)² - 4

• y = (x + 2)² + 7

• y = (x + 2)²

• y = (x - 2)² - 7

Answer explanation

To convert y = x^2 + 4x + 11 to vertex form, complete the square: y = (x + 2)^2 + 7. The correct choice is y = (x + 2)^2 + 7, which shows the vertex at (-2, 7).

Answer explanation

To simplify \( \sqrt{80x^2y^4} \), factor it as \( \sqrt{16 \cdot 5 \cdot x^2 \cdot y^4} = \sqrt{16} \cdot \sqrt{5} \cdot x \cdot y^2 = 4xy^2\sqrt{5} \). Thus, the correct answer is \( 4xy^2\sqrt{5} \).