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# Plotting quadratic graphs
- URL: https://www.esheets.io/plotting-quadratic-graphs/
- Published: 2026-08-14T10:29:33.000Z
- Updated: 2026-08-14T10:29:33.000Z
- Author: Richard Linnington
- Tags: Algebra, Maths

Practise completing tables of values and plotting the coordinates to draw smooth quadratic graphs. You'll work with equations like $y = x^2$ and $y = x^2 - 2x + 3$, learning to substitute negative values carefully and identify when a point has been plotted incorrectly. [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

This worksheet provides interactive practice for plotting quadratic graphs. You will complete missing values in a table, plot the points on a grid, and see the smooth parabola appear when your coordinates are correct.

The questions progress from simple $y=x^2$ graphs to full quadratics, including downward-opening curves and exercises where you must spot and correct deliberate plotting errors.

#### What you’ll practise

- Substituting positive and negative $x$-values into a quadratic equation.
- Completing a table of values accurately.
- Plotting coordinate pairs on a Cartesian grid.
- Recognising the characteristic smooth parabolic shape, opening upwards or downwards.
- Identifying and correcting common misplotted points.

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example.

# Plotting quadratic graphs

Complete the table of values and plot the points. When your points are correct, the smooth curve will be shown.

## Topic guide

A quadratic graph represents an equation where the highest power of $x$ is 2, such as $y = x^2$ or $y = 2x^2 - 3x + 1$. When plotted, a quadratic graph forms a smooth, symmetrical curve called a **parabola**. It will look like a 'U' shape (if the $x^2$ term is positive) or an 'n' shape (if the $x^2$ term is negative).

### How to plot a quadratic graph

1. **Complete the table of values:** Substitute each $x$-value from the table into the equation to find the corresponding $y$-value.
2. **Write the coordinates:** Pair each $x$-value with its $y$-value to form coordinate pairs $(x, y)$.
3. **Plot the points:** Mark each coordinate pair on the grid.
4. **Draw the curve:** Join the points with a single, smooth, flowing curve. Do not use a ruler to connect the points with straight lines.

### Worked example

Complete the table of values and plot the graph of $y = x^2 - 2x - 3$ for values of $x$ from $-2$ to $4$.

First, substitute the $x$-values into the equation. Be very careful when substituting negative numbers: squaring a negative number gives a positive result.

- When $x = -2$: $y = (-2)^2 - 2(-2) - 3 = 4 + 4 - 3 = 5$
- When $x = -1$: $y = (-1)^2 - 2(-1) - 3 = 1 + 2 - 3 = 0$
- When $x = 0$: $y = (0)^2 - 2(0) - 3 = 0 - 0 - 3 = -3$
- When $x = 1$: $y = (1)^2 - 2(1) - 3 = 1 - 2 - 3 = -4$
- When $x = 2$: $y = (2)^2 - 2(2) - 3 = 4 - 4 - 3 = -3$
- When $x = 3$: $y = (3)^2 - 2(3) - 3 = 9 - 6 - 3 = 0$
- When $x = 4$: $y = (4)^2 - 2(4) - 3 = 16 - 8 - 3 = 5$

The completed table gives us the coordinates: $(-2, 5)$, $(-1, 0)$, $(0, -3)$, $(1, -4)$, $(2, -3)$, $(3, 0)$ and $(4, 5)$.

Plotting these points and joining them with a smooth curve reveals a symmetrical U-shaped parabola with its lowest point (vertex) at $(1, -4)$.

### Common mistakes to avoid

- **Sign errors with negative numbers:** Remember that $(-3)^2$ is $9$, not $-9$. Also, subtracting a negative number is equivalent to adding a positive number.
- **Drawing straight lines:** A quadratic graph is a curve. Do not join the plotted points with straight line segments using a ruler.
- **A pointed vertex:** The bottom (or top) of the curve should be rounded and smooth, not a sharp point.
- **Misplotted points:** Because quadratic graphs are symmetrical, a single misplotted point will usually stand out because it disrupts the smooth parabolic shape. If one point breaks the pattern, double-check your substitution for that $x$-value.