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 given by the equation $y = x^2 + 2x - 8$ , calculate the points where the graph intersects the axes.

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

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

The parabola intersects the y-axis at the point $(0, -8)$ .

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

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

Factor the quadratic expression:

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

Set each individual factor to zero and solve:

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

The parabola intersects the x-axis at the points $(-4, 0)$ and $(2, 0)$ .

Updated 2026-04-21

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