What are the x and y intercepts of the graph of y = x² + 7x + 12?

To find the x and y intercepts of the graph of the equation y = x² + 7x + 12, we need to follow a few steps.

Finding the x-intercepts

The x-intercepts occur where the graph crosses the x-axis, which means at these points, y = 0.

So, we set the equation to zero:

0 = x² + 7x + 12

Now, we will factor the quadratic equation:

(x + 3)(x + 4) = 0

Setting each factor to zero gives us:

x + 3 = 0  →  x = -3

x + 4 = 0  →  x = -4

Thus, the x-intercepts are at the points (-3, 0) and (-4, 0).

Finding the y-intercept

The y-intercept occurs where the graph crosses the y-axis, which corresponds to when x = 0.

We substitute x = 0 into the equation:

y = 0² + 7(0) + 12 = 12

Thus, the y-intercept is at the point (0, 12).

Final Summary

The x-intercepts of the graph are (-3, 0) and (-4, 0), while the y-intercept is (0, 12).