Answer:
To find the x-intercepts of the parabola defined by the equation y = 2x² - 8x + 10, you need to set y equal to zero (because x-intercepts occur when y is zero) and solve for x.
So, you have:
0 = 2x² - 8x + 10
Now, you can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / (2a)
In this equation, a = 2, b = -8, and c = 10. Plug these values into the formula:
x = (-(-8) ± √((-8)² - 4 * 2 * 10)) / (2 * 2)
x = (8 ± √(64 - 80)) / 4
x = (8 ± √(-16)) / 4
Since the discriminant (the value inside the square root) is negative, there are no real solutions, which means this parabola does not have x-intercepts in the real number system.
So, there are no ordered pairs (x1, y1) and (x2, y2) for x-intercepts because there are no x-intercepts for this parabola in the real number system.
Explanation:
Certainly, let's find the x-intercepts step by step for the equation:
y = 2x² - 8x + 10
Step 1: Set y to zero because x-intercepts occur when y equals zero:
0 = 2x² - 8x + 10
Step 2: Now, we want to solve this equation for x. We can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this formula:
a is the coefficient of the x² term (which is 2 in this case).
b is the coefficient of the x term (which is -8).
c is the constant term (which is 10).
Step 3: Plug the values of a, b, and c into the formula:
x = (-(-8) ± √((-8)² - 4 * 2 * 10)) / (2 * 2)
Step 4: Simplify the equation inside the square root:
x = (8 ± √(64 - 80)) / 4
x = (8 ± √(-16)) / 4
Step 5: Now, notice that we have a square root of a negative number (√(-16)). In the real number system, we can't take the square root of a negative number. This means there are no real solutions for x.
Step 6: Since there are no real solutions, there are no x-intercepts for this parabola in the real number system. Therefore, there are no ordered pairs (x1, y1) and (x2, y2) for x-intercepts in this case.