How do you find the x and y intercepts of the graph of the equation y = x² + 3x + 10?

by

To find the x and y intercepts of the graph of the equation y = x² + 3x + 10, we can follow these steps:

X-Intercepts

The x-intercepts occur where the graph crosses the x-axis. At these points, the value of y is zero. To find the x-intercepts, we set y to zero and solve for x:

0 = x² + 3x + 10

This is a quadratic equation. To solve it, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 1, b = 3, and c = 10. Plugging in these values:

x = (-(3) ± √((3)² - 4(1)(10))) / (2(1))

Calculating the discriminant:

(3)² - 4(1)(10) = 9 - 40 = -31

Since the discriminant is negative (-31), this indicates that there are no real x-intercepts. The graph does not cross the x-axis.

Y-Intercepts

The y-intercept occurs where the graph crosses the y-axis. At this point, the value of x is zero. To find the y-intercept, we set x to zero and solve for y:

y = (0)² + 3(0) + 10

Calculating this gives:

y = 10

So, the y-intercept is at the point (0, 10).

Summary

  • The graph of y = x² + 3x + 10 has no real x-intercepts.
  • The y-intercept is at the point (0, 10).

Leave a Comment