Quadratic Vertex Calculator
Vertex, axis, intercepts and vertex form from a, b, c.
Enter your values
Enter the a you are working with.
Enter the b you are working with.
Enter the c you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Vertex
- (2, -5)
- Vertex form
- y = 2(x − 2)² − 5
- Axis of symmetry
- x = 2
- Opens
- Upward — vertex is the minimum
- x-intercepts
- 0.4189 and 3.5811
- y-intercept
- 3
Quick answer
The vertex of y = ax² + bx + c sits at x = −b ÷ 2a, and substituting that x back into the equation gives the vertex's y value.
x = −b ÷ 2a
At a glance
| What it does | Vertex, axis, intercepts and vertex form from a, b, c. |
|---|---|
| Category | Math |
| Inputs needed | a, b, c |
| Main output | Vertex |
| Formula | x = −b ÷ 2a |
| Cost | Free — no sign-up, no download |
How to use the Quadratic Vertex Calculator
- 1Enter a, b and c from y = ax² + bx + c.
- 2Read the vertex and the axis of symmetry.
- 3Use the vertex form for graphing or for optimisation problems.
Inputs explained
- a
- Enter the a you are working with.
- b
- Enter the b you are working with.
- c
- Enter the c you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- a2
- b-8
- c3
Results
- Vertex(2, -5)
- Vertex formy = 2(x − 2)² − 5
- Axis of symmetryx = 2
- OpensUpward — vertex is the minimum
- x-intercepts0.4189 and 3.5811
- y-intercept3
Frequently asked questions
How do I know if the vertex is a max or a min?
If a is positive the parabola opens upward and the vertex is the lowest point; if a is negative it is the highest.
What if there are no real roots?
The parabola never crosses the x-axis — the discriminant b² − 4ac is negative.
What do I need to enter into the Quadratic Vertex Calculator?
Just 3 values: a, b, c. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Quadratic Vertex Calculator work out the answer?
The vertex of y = ax² + bx + c sits at x = −b ÷ 2a, and substituting that x back into the equation gives the vertex's y value. It applies the formula x = −b ÷ 2a and shows the working so you can check each step by hand.
Is the Quadratic Vertex Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.