1Cademy - Finding the Intercepts of $$y = x^2 - 2x

Example

Finding the Intercepts of $y = x^2 - 2x - 8$

To find the intercepts of the parabola described by the equation $y = x^2 - 2x - 8$ , determine where the graph crosses each axis.

Calculating the y-intercept: Substitute $x = 0$ into the equation and solve for $y$ :

$y = 0^2 - 2(0) - 8$ $y = -8$

This gives the y-intercept at the point $(0, -8)$ .

Calculating the x-intercepts: Substitute $y = 0$ into the equation and solve the resulting quadratic equation for $x$ :

$0 = x^2 - 2x - 8$

Solve by factoring the right side of the equation:

$0 = (x - 4)(x + 2)$

Apply the zero product property by setting each factor equal to zero:

$x - 4 = 0 \quad \text{or} \quad x + 2 = 0$

$x = 4 \quad \text{or} \quad x = -2$

This yields the x-intercepts at the points $(4, 0)$ and $(-2, 0)$ .

Updated 2026-04-21

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