What are the x and y intercepts of the graph of y = x^2 + 10x + 21?

To find the x-intercepts of the graph of the equation y = x² + 10x + 21, we need to set y to zero and solve for x. This gives us:

x2 + 10x + 21 = 0

We can factor this quadratic equation.

(x + 3)(x + 7) = 0

Setting each factor to zero gives:

x + 3 = 0           or    x + 7 = 0

This results in:

x = -3        and    x = -7

So, the x-intercepts are at the points (-3, 0) and (-7, 0).

Next, to find the y-intercept, we set x to zero in the original equation:

y = (0)2 + 10(0) + 21

This simplifies to:

y = 21

Thus, the y-intercept occurs at the point (0, 21).

In summary, the intercepts of the graph are:

• X-Intercepts: (-3, 0) and (-7, 0)
• Y-Intercept: (0, 21)