1Cademy - Finding the Intercepts of $$y = x^2 - 4x

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Finding the Intercepts of a Parabola

Example

Finding the Intercepts of $y = x^2 - 4x - 5$

To find the intercepts of the parabola given by the equation $y = x^2 - 4x - 5$ :

Finding the y-intercept: Let $x = 0$ and solve for $y$ :

$y = 0^2 - 4(0) - 5$ $y = -5$

The y-intercept is the point $(0, -5)$ .

Finding the x-intercepts: Let $y = 0$ and solve the resulting quadratic equation for $x$ :

$0 = x^2 - 4x - 5$

Solve by factoring the trinomial:

$0 = (x - 5)(x + 1)$

Apply the Zero Product Property by setting each factor equal to zero:

$x - 5 = 0 \quad \text{or} \quad x + 1 = 0$ $x = 5 \quad \text{or} \quad x = -1$

The x-intercepts are the points $(5, 0)$ and $(-1, 0)$ .

Updated 2026-04-21

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OpenStax Elementary Algebra

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