Find the domain and range of y = -2x^2 + 8x - 9

D: all real numbers; R: y ≤ -1

Find the domain and range of y = x^2 - 7

D: all real numbers; R: y ≥ -7

Find the domain and range of y = -2x^2 + 12x - 21

D: all real numbers; R: y ≤ -3

Find the domain and range of y = 2x^2 - 12x + 26

D: all real numbers; R: y ≥ 8

Find the domain and range of y = x^2 - 4x + 5

D: all real numbers; R: y ≥ 1

Find the domain and range of y = -3x^2 + 12x - 14

D: all real numbers; R: y ≤ -2

Find the domain and range of y = -(x - 1)^2 + 4

D: all real numbers; R: y ≤ 4

Worksheets · Algebra 2

Algebra 2 properties of parabolas worksheet

For y = ax² + bx + c the axis of symmetry is x = -b over 2a, the vertex sits on it, and the y-intercept is c. The sign of a says which way it opens, and the vertex is then the minimum or the maximum, which also fixes the range.

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Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Properties of Parabolas Date Period Find what is asked for each parabola. Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - 2 x^{2} - 20 x - 50$ Find the maximum or minimum value of $y = - 3 x^{2} + 30 x - 79$ Find the domain and range of $y = - 2 x^{2} + 8 x - 9$ Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - 3 x^{2}$ Find the maximum or minimum value of $y = x^{2} + 2 x - 3$ Find the domain and range of $y = x^{2} - 7$ Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = 2 x^{2} - 12 x + 14$ Find the maximum or minimum value of $y = - x^{2} - 10 x - 26$ Find the domain and range of $y = - 2 x^{2} + 12 x - 21$ Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - x^{2} + 4 x - 3$ Find the maximum or minimum value of $y = 3 x^{2} + 18 x + 31$ Find the domain and range of $y = 2 x^{2} - 12 x + 26$ Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - x^{2} + 6 x - 15$ Find the maximum or minimum value of $y = - x^{2} - 2 x - 5$ Find the domain and range of $y = x^{2} - 4 x + 5$ Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = x^{2} + 6 x + 1$ Find the maximum or minimum value of $y = - 2 x^{2} + 16 x - 36$ Find the domain and range of $y = - 3 x^{2} + 12 x - 14$ Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - x^{2} + 4 x + 4$ Find the maximum or minimum value of $y = - 3 x^{2} + 12 x - 5$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Properties of Parabolas

Date Period

Find what is asked for each parabola.

Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - 2 x^{2} - 20 x - 50$
Find the maximum or minimum value of $y = - 3 x^{2} + 30 x - 79$
Find the domain and range of $y = - 2 x^{2} + 8 x - 9$
Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - 3 x^{2}$
Find the maximum or minimum value of $y = x^{2} + 2 x - 3$
Find the domain and range of $y = x^{2} - 7$
Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = 2 x^{2} - 12 x + 14$
Find the maximum or minimum value of $y = - x^{2} - 10 x - 26$
Find the domain and range of $y = - 2 x^{2} + 12 x - 21$
Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - x^{2} + 4 x - 3$
Find the maximum or minimum value of $y = 3 x^{2} + 18 x + 31$
Find the domain and range of $y = 2 x^{2} - 12 x + 26$
Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - x^{2} + 6 x - 15$
Find the maximum or minimum value of $y = - x^{2} - 2 x - 5$
Find the domain and range of $y = x^{2} - 4 x + 5$
Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = x^{2} + 6 x + 1$
Find the maximum or minimum value of $y = - 2 x^{2} + 16 x - 36$
Find the domain and range of $y = - 3 x^{2} + 12 x - 14$
Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - x^{2} + 4 x + 4$
Find the maximum or minimum value of $y = - 3 x^{2} + 12 x - 5$



Sigma Prep · sigmaprep.io/worksheets Name Properties of ParabolasAnswer keyVersion 1 Date Period Find what is asked for each parabola. Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - 2 x^{2} - 20 x - 50$ Vertex $(- 5, 0)$ ; axis $x = - 5$ ; $y$ -int $(0, - 50)$ ; opens down Find the maximum or minimum value of $y = - 3 x^{2} + 30 x - 79$ Maximum, $- 4$ Find the domain and range of $y = - 2 x^{2} + 8 x - 9$ $D :$ all real numbers; $R : y \leq - 1$ Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - 3 x^{2}$ Vertex $(0, 0)$ ; axis $x = 0$ ; $y$ -int $(0, 0)$ ; opens down Find the maximum or minimum value of $y = x^{2} + 2 x - 3$ Minimum, $- 4$ Find the domain and range of $y = x^{2} - 7$ $D :$ all real numbers; $R : y \geq - 7$ Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = 2 x^{2} - 12 x + 14$ Vertex $(3, - 4)$ ; axis $x = 3$ ; $y$ -int $(0, 14)$ ; opens up Find the maximum or minimum value of $y = - x^{2} - 10 x - 26$ Maximum, $- 1$ Find the domain and range of $y = - 2 x^{2} + 12 x - 21$ $D :$ all real numbers; $R : y \leq - 3$ Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - x^{2} + 4 x - 3$ Vertex $(2, 1)$ ; axis $x = 2$ ; $y$ -int $(0, - 3)$ ; opens down Find the maximum or minimum value of $y = 3 x^{2} + 18 x + 31$ Minimum, $4$ Find the domain and range of $y = 2 x^{2} - 12 x + 26$ $D :$ all real numbers; $R : y \geq 8$ Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - x^{2} + 6 x - 15$ Vertex $(3, - 6)$ ; axis $x = 3$ ; $y$ -int $(0, - 15)$ ; opens down Find the maximum or minimum value of $y = - x^{2} - 2 x - 5$ Maximum, $- 4$ Find the domain and range of $y = x^{2} - 4 x + 5$ $D :$ all real numbers; $R : y \geq 1$ Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = x^{2} + 6 x + 1$ Vertex $(- 3, - 8)$ ; axis $x = - 3$ ; $y$ -int $(0, 1)$ ; opens up Find the maximum or minimum value of $y = - 2 x^{2} + 16 x - 36$ Maximum, $- 4$ Find the domain and range of $y = - 3 x^{2} + 12 x - 14$ $D :$ all real numbers; $R : y \leq - 2$ Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - x^{2} + 4 x + 4$ Vertex $(2, 8)$ ; axis $x = 2$ ; $y$ -int $(0, 4)$ ; opens down Find the maximum or minimum value of $y = - 3 x^{2} + 12 x - 5$ Maximum, $7$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Properties of ParabolasAnswer keyVersion 1

Date Period

Find what is asked for each parabola.

Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - 2 x^{2} - 20 x - 50$ Vertex $(- 5, 0)$ ; axis $x = - 5$ ; $y$ -int $(0, - 50)$ ; opens down
Find the maximum or minimum value of $y = - 3 x^{2} + 30 x - 79$ Maximum, $- 4$
Find the domain and range of $y = - 2 x^{2} + 8 x - 9$ $D :$ all real numbers; $R : y \leq - 1$
Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - 3 x^{2}$ Vertex $(0, 0)$ ; axis $x = 0$ ; $y$ -int $(0, 0)$ ; opens down
Find the maximum or minimum value of $y = x^{2} + 2 x - 3$ Minimum, $- 4$
Find the domain and range of $y = x^{2} - 7$ $D :$ all real numbers; $R : y \geq - 7$
Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = 2 x^{2} - 12 x + 14$ Vertex $(3, - 4)$ ; axis $x = 3$ ; $y$ -int $(0, 14)$ ; opens up
Find the maximum or minimum value of $y = - x^{2} - 10 x - 26$ Maximum, $- 1$
Find the domain and range of $y = - 2 x^{2} + 12 x - 21$ $D :$ all real numbers; $R : y \leq - 3$
Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - x^{2} + 4 x - 3$ Vertex $(2, 1)$ ; axis $x = 2$ ; $y$ -int $(0, - 3)$ ; opens down
Find the maximum or minimum value of $y = 3 x^{2} + 18 x + 31$ Minimum, $4$
Find the domain and range of $y = 2 x^{2} - 12 x + 26$ $D :$ all real numbers; $R : y \geq 8$
Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - x^{2} + 6 x - 15$ Vertex $(3, - 6)$ ; axis $x = 3$ ; $y$ -int $(0, - 15)$ ; opens down
Find the maximum or minimum value of $y = - x^{2} - 2 x - 5$ Maximum, $- 4$
Find the domain and range of $y = x^{2} - 4 x + 5$ $D :$ all real numbers; $R : y \geq 1$
Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = x^{2} + 6 x + 1$ Vertex $(- 3, - 8)$ ; axis $x = - 3$ ; $y$ -int $(0, 1)$ ; opens up
Find the maximum or minimum value of $y = - 2 x^{2} + 16 x - 36$ Maximum, $- 4$
Find the domain and range of $y = - 3 x^{2} + 12 x - 14$ $D :$ all real numbers; $R : y \leq - 2$
Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - x^{2} + 4 x + 4$ Vertex $(2, 8)$ ; axis $x = 2$ ; $y$ -int $(0, 4)$ ; opens down
Find the maximum or minimum value of $y = - 3 x^{2} + 12 x - 5$ Maximum, $7$

How to do these

Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = x^{2} - 6 x + 5$

Axis: x = 6 over 2, which is 3.
Vertex: y at x = 3 is 9 - 18 + 5, which is -4.
Intercept c = 5; a is positive so it opens up.

The answer is Vertex $(3, - 4)$ , axis $x = 3$ , $y$ -intercept $(0, 5)$ , opens up.

Where students go wrong

Losing the minus in -b over 2a. For y = x² - 6x + 5, b is -6, so the axis is at positive 3.

Also called vertex and axis of symmetry, maximum or minimum of a quadratic, range of a parabola or quadratic features.

What you can put on this worksheet

Vertex, axis, intercept, direction: Vertex, axis of symmetry, $y$ -intercept, and opens up or down: $y = - (x - 1)^{2} + 4$ → Vertex $(1, 4)$ ; axis $x = 1$ ; $y$ -int $(0, 3)$ ; opens down
The maximum or minimum value: Find the maximum or minimum value of $y = - x^{2} + 2 x + 3$ → Maximum, $4$
Domain and range: Find the domain and range of $y = - (x - 1)^{2} + 4$ → $D :$ all real numbers; $R : y \leq 4$

Questions about these worksheets

Yes. Every properties of parabolas sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the properties of parabolas questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 3: vertex, axis, intercept, direction, the maximum or minimum value and domain and range. Tick as many as you want and set how many of each, or let it spread them evenly.

Losing the minus in -b over 2a. For y = x² - 6x + 5, b is -6, so the axis is at positive 3.

Algebra 2 properties of parabolas worksheet

Select your difficulty

Properties of Parabolas

Properties of ParabolasAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

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