Algebra 1 Solving Quadratics Quiz – Free PDF

Contents

This algebra 1 solving quadratics quiz asks 10 multiple-choice questions on solving quadratic equations, and each answer comes with a short explanation.

Try these ten multiple-choice questions on quadratic equations: square roots, factoring, completing the square, the discriminant and a word problem. Each has one correct answer, and the explanation points out the usual slip.

Algebra 1Common Core: A-REI.B.4a · A-REI.B.4b · A-APR.B.3 · A-CED.A.1

🎯 Solving Quadratic Equations – Algebra 1 math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

Solve \(x^{2}=64\).

A \(x=8\)

B \(x=32\text{ or }x=-32\)

C \(x=8\text{ or }x=-8\)

D \(x=4\text{ or }x=-4\)

Question 2

Solve \((x-2)^{2}=9\). The number line shows the center.

Number line for \((x-2)^{2}=9\).

A \(x=11\text{ or }x=-7\)

B \(x=5\)

C \(x=-5\text{ or }x=1\)

D \(x=5\text{ or }x=-1\)

Question 3

What are the solutions of \((x+3)(x-8)=0\)?

A \(x=-3\text{ or }x=8\)

B \(x=3\text{ or }x=-8\)

C \(x=3\text{ or }x=8\)

D \(x=-3\text{ or }x=-8\)

Question 4

Solve \(x^{2}-x-12=0\).

A \(x=-4\text{ or }x=3\)

B \(x=4\text{ or }x=-3\)

C \(x=4\text{ or }x=3\)

D \(x=6\text{ or }x=-2\)

Question 5

The graph of \(y=x^{2}-6x+5\) is shown. What are the solutions of \(x^{2}-6x+5=0\)?

Graph of \(y=x^{2}-6x+5\).

A \(x=1\text{ or }x=5\)

B \(x=3\)

C \(x=5\text{ or }x=-1\)

D \(x=-1\text{ or }x=-5\)

Question 6

What number completes the square in \(x^{2}+14x\)?

A \(14\)

B \(49\)

C \(7\)

D \(196\)

Question 7

What is the discriminant of \(2x^{2}-3x+5=0\)?

A \(31\)

B \(-31\)

C \(49\)

D \(-11\)

Question 8

How many real solutions does \(x^{2}-4x+4=0\) have? The graph is shown.

Graph of \(y=x^{2}-4x+4\).

A Exactly two

B No real solutions

C Infinitely many

D Exactly one

Question 9

Which are the solutions of \(2x^{2}+x-3=0\)?

A \(x=-1\text{ or }x=\frac{3}{2}\)

B \(x=1\text{ or }x=\frac{3}{2}\)

C \(x=1\text{ or }x=-\frac{3}{2}\)

D \(x=-1\text{ or }x=-\frac{3}{2}\)

Question 10

A rectangle is 4 feet longer than it is wide, and its area is 45 square feet. What is its width?

Rectangle model for the problem.

A \(5\text{ ft}\)

B \(9\text{ ft}\)

C \(-9\text{ ft}\)

D \(11.25\text{ ft}\)

🎉 Quiz complete!

0 / 10

How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Standards A-REI.B.4a, A-REI.B.4b, A-APR.B.3 and A-CED.A.1: solve quadratics, relate zeros to graphs, and model with equations.
Zero-product property: if \(mn=0\), then \(m=0\) or \(n=0\).
Completing the square adds \((\frac{b}{2})^{2}\) to both sides of \(x^{2}+bx=k\).
The quadratic formula is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\).
The discriminant \(b^{2}-4ac\) is positive, zero or negative for two, one or no real solutions.