Question

Given the function f(x)=−2x ²+18x−28, algebraically determine the x-intercepts and the y Intercept a. The x-intercepts are b. The y-intercept is

Answer 1

The x-intercepts of the function f(x) = -2x² + 18x - 28 are found using the quadratic formula, and the y-intercept is found by evaluating the function at x = 0, which results in the point (0, -28).

Step-by-step explanation:

To find the x-intercepts of the function f(x) = -2x² + 18x - 28, we set f(x) equal to zero and solve for x. This gives us a quadratic equation that we can solve using the quadratic formula, x = [-b ± √(b² - 4ac)] / (2a), where a = -2, b = 18, and c = -28. After substituting these values into the quadratic formula, we calculate the x-intercepts.

The y-intercept is found by evaluating f(x) at x = 0. For the given function, this simply requires calculating f(0), which will give us the point at which the graph crosses the y-axis.

Let's perform these calculations:

1. To find the x-intercepts, substitute the values into the quadratic formula:

x = [18 ± √(18² - 4*(-2)*(-28))] / (2*(-2))

1. For the y-intercept:

f(0) = -2(0)² + 18(0) - 28 = -28

Thus, the y-intercept of the function is (0, -28).

Learn more about x-intercepts and y-intercept