Lelfy

Quadratic Equations Quiz

Quadratic Equations: ten practice questions on roots, graphs, and applied calculations. Every answer is explained.

Free, with no sign-up.

ByLelfy Editorial Team

For High school students and adults reviewing the topic.

About 14 minutes. 10 questions.

How does it work?

  1. Choose one answer or enter a number in the stated unit, then check it.
  2. Read the explanation after answering.
  3. Round only the final answer to the precision requested.

What will you get?

Review your score and the reasoning for each answer.

Question 1A rectangle has width x m and length (x + 5) m, with area 84 m². Find its positive width in m, rounded to two decimal places.

Answers within 0.005 m of the expected value are accepted.

Question 2For 2x² − 5x − 4 = 0, find the larger root as a number rounded to three decimal places.

Answers within 0.0005 of the expected value are accepted.

Question 3A model uses y = 3x² + 8x + 2. Calculate b² − 4ac as a whole number.

Answers within 0.5 of the expected value are accepted.

Question 4A profit model is P(x) = −2x² + 28x − 30. Find the x-coordinate of its vertex as a number rounded to two decimal places.

Answers within 0.005 of the expected value are accepted.

Question 5One curved panel follows y = 2x² − 3x + 7, with x and y measured in m. Find y at x = 4 m, rounded to two decimal places in m.

Answers within 0.005 m of the expected value are accepted.

Question 6An idealized dropped object has height h(t) = 44.1 − 4.9t² in m, with t in s after release. Find the time it reaches the ground in s, rounded to two decimal places.

Answers within 0.005 s of the expected value are accepted.

Question 7Which candidate satisfies x² − 3x − 18 = 0?
Question 8Which product expands to x² + 3x − 28?
Question 9Which equation has no real solution?
Question 10A designer wants x² − 12x + c = 0 to have a repeated root. Which value of c works?

Answer every question to see and share your score.

Read the topic guide