Question

What are the x-intercepts, rounded to the nearest tenth if necessary, of the function y = one-tenthx2 – 15? check all that apply.

O (–12.2, 0)
O (–10, 0)
O (0, –15)
O (10, 0)
O (12.2, 0)

Answer 1

To find the x-intercepts of the quadratic function y = one-tenthx^2 – 15, we solve the equation 0 = one-tenth x^2 – 15, which leads to x^2 = 150. Taking the square root gives x ≈ 12.2 and x ≈ -12.2, so the x-intercepts are (12.2, 0) and (-12.2, 0).

Step-by-step explanation:

Finding the X-intercepts of a Quadratic Function

To find the x-intercepts of a quadratic function, we set y to zero and solve for x. In the given function y = one-tenthx2 – 15, this means solving the quadratic equation 0 = one-tenth x2 – 15.

This simplifies to x2 = 150, which we can solve by taking the square root of both sides.

The square root of 150 gives us two solutions: x = √150 and x = -√150. Rounding these to the nearest tenth, we have x ≈ 12.2 and x ≈ -12.2, which correspond to the x-intercepts (12.2, 0) and (-12.2, 0), respectively.

The option (0, –15) represents the y-intercept, which is not what we're looking for in this case.

The y-intercept occurs where the graph crosses the y-axis, which is when x=0.

Hence, the correct x-intercept options are (12.2, 0) and (-12.2, 0). The given function does not have x-intercepts at (10, 0) or (-10, 0).