How do you find the x-intercepts of the equation y = 2x² + 3x – 20?

by

Finding the X-Intercepts of the Equation

The x-intercepts of a parabola are the points where the graph intersects the x-axis. This occurs when the value of y is equal to zero. To find the x-intercepts of the equation y = 2x² + 3x – 20, we need to set y to zero and solve for x:

Step 1: Set the equation to zero

0 = 2x² + 3x - 20

This is a quadratic equation in the standard form ax² + bx + c = 0, where:

  • a = 2
  • b = 3
  • c = -20

Step 2: Use the quadratic formula

To find the values of x, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting in our values:

x = (–3 ± √(3² - 4(2)(–20))) / (2(2))

Now, calculate the discriminant:

  • 3² = 9
  • 4 × 2 × –20 = –160
  • So, 9 + 160 = 169

The discriminant is positive (169), which means there will be two distinct real roots.

Step 3: Calculate the roots

x = (–3 ± √169) / 4

Since √169 = 13, we have:

x = (–3 ± 13) / 4

Now calculate the two possible values of x:

  1. For the positive root:
    2. x = (–3 + 13) / 4 = 10 / 4 = 2.5
  2. For the negative root:
    3. x = (–3 - 13) / 4 = –16 / 4 = –4

Conclusion

The x-intercepts of the equation y = 2x² + 3x – 20 are:

  • (2.5, 0)
  • (–4, 0)

Leave a Comment