Grade 11 · Math · Algebra 2

11th grade Quadratic inequalities: graph and solve worksheet

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Quadratic inequalities: graph and solve

Grade 11 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Ren solves x² < 2x + 15. What is the answer, written like 2 < x < 9?
Zee solves x² ≥ 4x + 12. What is the answer, written like x < 1 or x > 6?
Esme solves 2x² > 8x. What is the answer, written like x < 1 or x > 6?
Luz launches a ball. Its height is h = -16t² + 80t feet, t seconds after launch. For how many seconds is it higher than 64 feet?
Milo launches a model rocket. Its height is h = -16t² + 96t feet, t seconds after launch. For how many seconds is it higher than 80 feet?
Noah launches a water rocket. Its height is h = -5t² + 40t meters, t seconds after launch. For how many seconds is it higher than 60 meters?
Pia launches a toy rocket. Its height is h = -5t² + 35t meters, t seconds after launch. For how many seconds is it higher than 30 meters?
8.
Ren checks the discriminant of x² + 4x + 5 first. Which is the solution of x² + 4x + 5 < 0?
- No solution
- -5 < x < 1
- x = -2 only
- All real numbers
9.
Esme checks the discriminant of -x² + 2x − 3 first. Which is the solution of -x² + 2x − 3 < 0?
- All real numbers
- -1 < x < 3
- No solution
- x = 1 only
10.
Jun checks the discriminant of x² − 14x + 49 first. Which is the solution of x² − 14x + 49 ≤ 0?
- No solution
- All real numbers
- x = 7 only
- x ≤ 7

Quadratic inequalities: graph and solve. Every version has 10 questions, and the answer key prints on the second page.

I can find the zero rows and say where a quadratic is above or below 0.
I can solve a quadratic inequality and write the answer like -2 < x < 4 or x < 1 or x > 6.
I can say how long a ball or rocket stays above a height.

Standard: A-REI.B.4, A-CED.A.1

zero rows: The inputs where the output is 0; the boundary of the answer.

between: The part of the number line from one zero to the other.

outside: The two parts beyond the zeros, joined by "or".

touch point: The one zero of a perfect square, where the graph just touches.

Your child found the right zeros but shaded the wrong side of them.

Your child picked a zero of the product, where it equals 0.

Your child took the signs in the brackets as the zeros.

Ask: is the parabola above or below the axis between its zeros?

Ask: is 0 less than 0?

Ask: what value of x makes (x + 2) equal 0?

What is the most common mistake with quadratic inequalities: graph and solve?

Your child found the right zeros but shaded the wrong side of them.

How can I help my child with quadratic inequalities: graph and solve?

Ask: is the parabola above or below the axis between its zeros?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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