Graphing calculator example

Explore a quadratic function with a slider

For y = ax² − 4, the coefficient a controls the direction and vertical stretch of the graph. Move the slider and compare matching positive and negative x values.

Try it on the graph

y = ax² − 4

Real-valued inputs

Coefficient a 1

Solid: current graph. Dashed: starting graph. Axes use the labeled scales.

Select a row to inspect its point
x	y
	0
	-3
	-4
	-3
	0

Selected point: (0, -4)

Values are rounded to seven significant digits.

Work one row: a = 1 and x = 2

Substitute a = 1 and x = 2 into y = ax² − 4.
Square x first: 2² = 4. Multiply by 1, then subtract 4. The result is y = 0.
So (2, 0) is an x-intercept. The input x = −2 also gives 0 because (−2)² = 4.

What to notice

For nonzero a, the vertex stays at (0, −4) and the graph is symmetric about the y-axis.

Positive a opens the parabola upward; negative a opens it downward. Increasing |a| stretches it vertically, making it look narrower at a fixed height.

At a = 0, the expression becomes y = −4. It is a horizontal line, not a quadratic function.

Check your understanding

Set a = −1 and inspect x = 2. The output is −8. Compare it with the value at x = −2.

Keep exploring

The full calculator lets you edit equations, add more curves, set axis bounds, and share or export your graph. The examples here use ordinary real-number arithmetic; graph lines and computed values are numerical approximations.

Open the graphing calculator →