Algebra 2 — Semester 1
Free Practice · 10 Questions · 20 min
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Question 1 of 10
Michigan Standards 4A-4FEasy Diagram

How many real zeros does the parabola show?

A1
B2
C0
D4
Explanation
Two distinct x-intercepts → discriminant > 0 → 2 real zeros.
Question 2 of 10
Michigan Standards 4A-4FEasy Diagram

How many real roots does the parabola have?

A2
B0 (no real roots)
C4
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
Michigan Standards 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 4 of 10
Michigan Standards 6A-6LEasy Diagram

Identify the function.

Af(x) = √x
Bf(x) = −|x| (V opens downward)
Cf(x) = x²
Df(x) = |x|
Explanation
Sharp corner (V-shape) opening downward indicates y = −|x|.
Question 5 of 10
Michigan Standards 4A-4FEasy Diagram

Find the vertex of the parabola.

(1, −3)
A(3, 1)
B(−1, 3)
C(0, 0)
D(1, −3)
Explanation
Vertex of an upward-opening parabola is the lowest point: (1, −3) as labeled.
Question 6 of 10
Michigan Standards 6A-6LEasy Diagram

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

−33
A−3 < x < 3
Bx = −3 or x = 3
Cx = 3 only
Dno solution
Explanation
Two filled dots indicate two distinct solutions: ±3.
Question 7 of 10
Michigan Standards 2A-2IEasy Diagram

Which transformation produces this graph from y = x²?

AHorizontal shift right
BReflection across the x-axis
CVertical shift down
DReflection across the y-axis
Explanation
Standard parabola opens up; this one opens down — that is y = −x², a reflection across the x-axis.
Question 8 of 10
Michigan Standards 1A-1GMedium Diagram

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

x + 6x + 4
A2x + 10
Bx² + 10x + 10
Cx² + 10x + 24
Dx² + 24
Explanation
(x + 4)(x + 6) = x² + 6x + 4x + 24 = x² + 10x + 24.
Question 9 of 10
Michigan Standards 1A-1GEasy
A rectangle has length 2x + 3 and width x − 1. Which polynomial represents its area?
A2x² + 4x − 3
B2x² + 5x − 3
C2x² − x − 3
D2x² + x − 3
Explanation
(2x + 3)(x − 1) = 2x² − 2x + 3x − 3 = 2x² + x − 3.
Question 10 of 10
Michigan Standards 1A-1GEasy Diagram

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

2w + 5w
A2w + 5w
Bw² + 5
C2w² + 5
D2w² + 5w
Explanation
Area = width × length = w(2w + 5) = 2w² + 5w.

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