X Intercepts Of Parabolas - MyQBook

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High School x- intercept(s) of parabolas:

The x-intercepts of a parabola are the points or point where the parabola intersects the x-axis. A parabola can have 0, 1 or 2 x-intercepts as shown below.

When the parabola has only one x-intercept, then the x-axis is said to be a tangent to the parabola. At any x-intercept of a parabola, the value of y = 0. This means, if we set y = 0 in the equation of the parabola y = ax2 + bx + c and solve the resulting quadratic equation ax2 + bx + c = 0 for the values of x, we can find the values of the x-intercepts. Also the value of the discriminant b2 – 4ac in the quadratic equation ax2 + bx + c = 0 tells us the nature of the roots. Finding the number of x-intercepts of a parabola: Hence, to find the number of x-intercepts in a parabola follow the steps below:

For example, say you need to find the number of x-intercepts of the parabola y = x2 + 5x + 6. Let’s try another example: find the number of x intercepts of the function y = (x – 3)2 + 3. Finding the x-intercepts of a parabola: As discussed above, the x-intercepts of a parabola y = ax2 + bx + c can be easily found by finding the roots of the quadratic equation ax2 + bx + c = 0. So, to find the x-intercept(s) of a parabola, follow the steps below:

For example: say you need to find the x-intercept(s) of the parabola y = x2 – 4x + 4.

Let’s try another example: find the x-intercepts of the function y = 2x2 + 7x + 3.

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