Question

Find the x-intercepts of the graph of the equation. $$y=x^{2}+8 x+12$$

Short answer

The x-intercepts of the graph of the equation \(y=x^{2}+8 x+12\) are x=-2 and x=-6.

Step-by-step solution

Set the Equation Equal to Zero

To find the x-intercepts, one will need to solve the equation for when y is zero. Thus, the equation becomes \(0=x^{2}+8x+12\).

Solve the Equation

The equation is a quadratic equation in the standard form \(ax^2 + bx + c = 0\). In this case, a = 1, b = 8, and c = 12. It can be solved for \(x\) by using the quadratic formula \(x = [ -b ± sqrt(b^2 - 4ac)]/2a\). Given the values of a, b, and c, the quadratic formula becomes \(x = [ -8 ± sqrt(8^2 - 4.1.12)]/2.1\), which simplifies to \(x=-4±sqrt{4}\).

Find the X-intercepts

Evaluate the expression in step 2 to get the two x-intercepts. This results in \(x=-4+2\) and \(x=-4-2\), thus yielding the x-intercepts x=-2 and x=-6.