1Cademy - Finding the Intercepts of $$y = 9x^2 + 12x + 4$$

Example

Finding the Intercepts of $y = 9x^2 + 12x + 4$

To find the intercepts of the parabola given by $y = 9x^2 + 12x + 4$ :

Finding the y-intercept: Let $x = 0$ and substitute it into the equation to solve for $y$ :

$y = 9(0)^2 + 12(0) + 4$ $y = 4$

The y-intercept is the point $(0, 4)$ .

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

$0 = 9x^2 + 12x + 4$

Solve the equation by factoring the perfect square trinomial:

$0 = (3x + 2)^2$

Use the Zero Product Property by setting the repeated factor equal to zero:

$3x + 2 = 0$ $3x = -2$ $x = -\frac{2}{3}$

Because there is only one real solution, the parabola touches the x-axis at a single point. The x-intercept is $(-\frac{2}{3}, 0)$ .

Updated 2026-04-21

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