Final answer:
To find the x-intercepts of the parabola y=-2x²+5x+2, we can use the quadratic formula (-b ± √(b²-4ac)) / (2a). Plugging in the values from the equation, we get x = (-5 ± √41) / -4. Therefore, the x-intercepts of the parabola are approximately -0.634 and 3.134.
Step-by-step explanation:
To find the x-intercepts of the parabola y=-2x²+5x+2, we set y equal to zero and solve for x:
0 = -2x² + 5x + 2
We can solve this quadratic equation by factoring or by using the quadratic formula:
x = (-b ± √(b²-4ac)) / (2a)
Plugging in the values from the equation, we get:
x = (-5 ± √(5²-4(-2)(2))) / (2(-2))
Simplifying this expression gives us the x-intercepts of the parabola:
x = (-5 ± √41) / -4
So, the x-intercepts of the parabola are approximately -0.634 and 3.134.11