Algebra 2 — Semester A Practice

Question 1 of 10

NYS 4A-4FEasy Diagram

Find the vertex of the parabola.

A(−1, 3)

B(3, 1)

C(1, −3)

D(0, 0)

Explanation

Vertex of an upward-opening parabola is the lowest point: (1, −3) as labeled.

Question 2 of 10

NYS 4A-4FEasy Diagram

How many real roots does the parabola have?

A0 (no real roots)

D1 (touches x-axis once)

Explanation

The parabola crosses the x-axis at two distinct points → two real roots → discriminant > 0.

Question 3 of 10

NYS 6A-6LEasy Diagram

Identify the function.

Af(x) = √x

Bf(x) = |x|

Cf(x) = x²

Df(x) = −|x| (V opens downward)

Explanation

Sharp corner (V-shape) opening downward indicates y = −|x|.

Question 4 of 10

NYS 2A-2IEasy Diagram

The graph below shows g(x). What is the parent function?

Af(x) = |x|

Bf(x) = x

Cf(x) = √x

Df(x) = x²

Explanation

Sharp V-shape with a corner at the vertex is the absolute-value parent function. Quadratic would be smooth.

Question 5 of 10

NYS 6A-6LEasy Diagram

What are the solutions to |x| = 3 shown on the number line?

A−3 < x < 3

Bno solution

Cx = 3 only

Dx = −3 or x = 3

Explanation

Two filled dots indicate two distinct solutions: ±3.

Question 6 of 10

NYS 2A-2IEasy Diagram

Which transformation produces this graph from y = x²?

AHorizontal shift right

BReflection across the y-axis

CVertical shift down

DReflection across the x-axis

Explanation

Standard parabola opens up; this one opens down — that is y = −x², a reflection across the x-axis.

Question 7 of 10

NYS 1A-1GMedium Diagram

A poster has dimensions (x + 4) by (x + 6). Which expression represents its area?

Ax² + 10x + 10

Bx² + 10x + 24

C2x + 10

Dx² + 24

Explanation

(x + 4)(x + 6) = x² + 6x + 4x + 24 = x² + 10x + 24.

Question 8 of 10

NYS 4A-4FEasy Diagram

How many real zeros does the parabola show?

Explanation

Two distinct x-intercepts → discriminant > 0 → 2 real zeros.

Question 9 of 10

NYS 1A-1GEasy

A rectangle has length 2x + 3 and width x − 1. Which polynomial represents its area?

A2x² + 5x − 3

B2x² − x − 3

C2x² + x − 3

D2x² + 4x − 3

Explanation

(2x + 3)(x − 1) = 2x² − 2x + 3x − 3 = 2x² + x − 3.

Question 10 of 10

NYS 1A-1GEasy Diagram

A garden plot is shown with width w and length 2w + 5. Which polynomial represents its area?

A2w² + 5w

B2w² + 5

C2w + 5w

Dw² + 5

Explanation

Area = width × length = w(2w + 5) = 2w² + 5w.

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