To find the x and y intercepts of a parabola, you need to follow these steps:
X-Intercepts
The x-intercepts are the points where the parabola crosses the x-axis. To find them, set the y value of the parabola’s equation to zero and solve for x. For example, if you have a parabola given by the equation y = ax^2 + bx + c, you’ll set y = 0.
This results in the equation:
0 = ax^2 + bx + c
You can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b² – 4ac)) / (2a)
The values of x you obtain from this equation will give you the x-intercepts, which can be two points, one point, or none, depending on the discriminant (b² – 4ac).
Y-Intercept
The y-intercept is the point where the parabola crosses the y-axis. To find it, simply set x = 0 in the parabola’s equation and solve for y. Using the same example:
y = a(0)^2 + b(0) + c = c
Thus, the y-intercept is the point (0, c).
In summary, to find the x-intercepts, set y to zero and solve for x. To find the y-intercept, set x to zero and solve for y. This process will help you understand where the parabola intersects the axes.