Question

Find the x-intercepts for the parabola defined by this equation:

[ y = -2x² - 8x + 10 ]
Write your answer as two ordered pairs: (x₁, y₁), (x₂, y₂).
Separate the values with a comma. Round, if necessary, to the nearest hundredth.

a) (1.43, 0), (-3.43, 0)
b) (2.15, 0), (-4.15, 0)
c) (-1.73, 0), (5.73, 0)
d) (0.65, 0), (-6.65, 0)

Answer 1

a) (1.43, 0), (-3.43, 0) through the quadratic equation, the x-intercepts are precisely determined, confirming the points where the parabola intersects the x-axis at approximately 1.43 and -3.43. This analysis assists in understanding the graphical representation of the given parabolic equation.

Explanation:

The x-intercepts of the parabola defined by the equation y = -2x² - 8x + 10 are found where y equals zero. To discover these points, set the equation equal to zero and solve for x using the quadratic formula or factoring. In this case, employing the quadratic formula, the x-intercepts are calculated as approximately 1.43 and -3.43, both yielding a y-coordinate of 0 when substituted back into the equation. These values confirm the points of intersection between the parabola and the x-axis.

The equation represents a downward-opening parabola due to the negative coefficient of x², and the x-intercepts identify the points where the curve intersects the x-axis. These intercepts mark the locations where the y-coordinate is zero, representing the points on the graph where the parabola crosses the x-axis. In this scenario, the calculated x-values correspond to the x-coordinates of the intercepts, while the y-values are zero as the curve crosses the x-axis.

Overall, through the quadratic equation, the x-intercepts are precisely determined, confirming the points where the parabola intersects the x-axis at approximately 1.43 and -3.43. This analysis assists in understanding the graphical representation of the given parabolic equation.