1Cademy - Finding the Intercepts of $$y = -x^2 - 12x

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Finding the Intercepts of a Parabola

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Finding the Intercepts of $y = -x^2 - 12x - 36$

To find the intercepts of the parabola $y = -x^2 - 12x - 36$ :

Finding the y-intercept: Substitute $x = 0$ into the equation and compute $y$ :

$y = -(0)^2 - 12(0) - 36$ $y = -36$

The y-intercept is the point $(0, -36)$ .

Finding the x-intercepts: Substitute $y = 0$ into the equation and solve for $x$ :

$0 = -x^2 - 12x - 36$

Factor out $-1$ to simplify the quadratic expression:

$0 = -(x^2 + 12x + 36)$

Recognize and factor the perfect square trinomial:

$0 = -(x + 6)^2$

Apply the Zero Product Property:

$x + 6 = 0$ $x = -6$

Since there is only one real solution, the parabola has exactly one x-intercept at the point $(-6, 0)$ .

Updated 2026-04-21

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OpenStax Elementary Algebra

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Elementary Algebra @ OpenStax

Ch.10 Quadratic Equations - Elementary Algebra @ OpenStax

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