Algebra 2 — Semester A Practice

Question 1 of 10

TEKS 4A-4F Easy Diagram

Find the vertex of the parabola.

A (3, 1)

B (−1, 3)

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

TEKS 2A-2I Easy Diagram

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

A f(x) = √x

B f(x) = x

C f(x) = x²

D f(x) = |x|

Explanation

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

Question 3 of 10

TEKS 1A-1G Easy Diagram

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

A 2w² + 5w

B w² + 5

C 2w + 5w

D 2w² + 5

Explanation

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

Question 4 of 10

TEKS 4A-4F Easy Diagram

How many real zeros does the parabola show?

A 2

B 1

C 0

D 4

Explanation

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

Question 5 of 10

TEKS 2A-2I Easy Diagram

Which transformation produces this graph from y = x²?

A Horizontal shift right

B Vertical shift down

C Reflection across the x-axis

D Reflection across the y-axis

Explanation

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

Question 6 of 10

TEKS 1A-1G Easy

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

A 2x² + x − 3

B 2x² + 5x − 3

C 2x² + 4x − 3

D 2x² − x − 3

Explanation

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

Question 7 of 10

TEKS 6A-6L Easy Diagram

Identify the function.

A f(x) = |x|

B f(x) = −|x| (V opens downward)

C f(x) = √x

D f(x) = x²

Explanation

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

Question 8 of 10

TEKS 6A-6L Easy Diagram

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

A x = 3 only

B x = −3 or x = 3

C −3 < x < 3

D no solution

Explanation

Two filled dots indicate two distinct solutions: ±3.

Question 9 of 10

TEKS 1A-1G Medium Diagram

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

A x² + 24

B x² + 10x + 10

C x² + 10x + 24

D 2x + 10

Explanation

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

Question 10 of 10

TEKS 4A-4F Easy Diagram

How many real roots does the parabola have?

A 4

B 2

C 1 (touches x-axis once)

D 0 (no real roots)

Explanation

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

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